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Question Number 22135 Answers: 1 Comments: 0

A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

$$\mathrm{A}\:\mathrm{mass}\:{m}\:\mathrm{hangs}\:\mathrm{with}\:\mathrm{the}\:\mathrm{help}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{string}\:\mathrm{wrapped}\:\mathrm{around}\:\mathrm{a}\:\mathrm{pulley}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{frictionless}\:\mathrm{bearing}.\:\mathrm{The}\:\mathrm{pulley}\:\mathrm{has} \\ $$$$\mathrm{mass}\:{m}\:\mathrm{and}\:\mathrm{radius}\:{R}.\:\mathrm{Assuming}\:\mathrm{pulley} \\ $$$$\mathrm{to}\:\mathrm{be}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{uniform}\:\mathrm{circular}\:\mathrm{disc},\:\mathrm{the} \\ $$$$\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{mass}\:{m},\:\mathrm{if}\:\mathrm{the} \\ $$$$\mathrm{string}\:\mathrm{does}\:\mathrm{not}\:\mathrm{slip}\:\mathrm{on}\:\mathrm{the}\:\mathrm{pulley},\:\mathrm{is} \\ $$

Question Number 22251 Answers: 1 Comments: 0

Reversible melting of solid benzene at 1 atm and normal melting point correspond to (1) q > 0 (2) w < 0 (3) ΔE > 0 (4) All of these

$$\mathrm{Reversible}\:\mathrm{melting}\:\mathrm{of}\:\mathrm{solid}\:\mathrm{benzene}\:\mathrm{at} \\ $$$$\mathrm{1}\:\mathrm{atm}\:\mathrm{and}\:\mathrm{normal}\:\mathrm{melting}\:\mathrm{point} \\ $$$$\mathrm{correspond}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{q}\:>\:\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{w}\:<\:\mathrm{0} \\ $$$$\left(\mathrm{3}\right)\:\Delta\mathrm{E}\:>\:\mathrm{0} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{All}\:\mathrm{of}\:\mathrm{these} \\ $$

Question Number 22295 Answers: 1 Comments: 0

The ionization potential of hydrogen is 13.6 eV/mole. Calculate the energy in kJ required to produce 0.1 mole of H^+ ions. Given, 1 eV = 96.49 kJ mol^(−1) )

$$\mathrm{The}\:\mathrm{ionization}\:\mathrm{potential}\:\mathrm{of}\:\mathrm{hydrogen}\:\mathrm{is} \\ $$$$\mathrm{13}.\mathrm{6}\:\mathrm{eV}/\mathrm{mole}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{energy}\:\mathrm{in} \\ $$$$\mathrm{kJ}\:\mathrm{required}\:\mathrm{to}\:\mathrm{produce}\:\mathrm{0}.\mathrm{1}\:\mathrm{mole}\:\mathrm{of}\:\mathrm{H}^{+} \\ $$$$\left.\mathrm{ions}.\:\mathrm{Given},\:\mathrm{1}\:\mathrm{eV}\:=\:\mathrm{96}.\mathrm{49}\:\mathrm{kJ}\:\mathrm{mol}^{−\mathrm{1}} \right) \\ $$

Question Number 22071 Answers: 1 Comments: 4

STATEMENT-1 : If an object is at rest then there should not be any friction on it. STATEMENT-2 : If an object is moving then the friction acting on it has to be kinetic. STATEMENT-3 : If an object is at rest then kinetic friction cannot act on it.

$$\mathrm{STATEMENT}-\mathrm{1}\::\:\mathrm{If}\:\mathrm{an}\:\mathrm{object}\:\mathrm{is}\:\mathrm{at} \\ $$$$\mathrm{rest}\:\mathrm{then}\:\mathrm{there}\:\mathrm{should}\:\mathrm{not}\:\mathrm{be}\:\mathrm{any}\:\mathrm{friction} \\ $$$$\mathrm{on}\:\mathrm{it}. \\ $$$$\mathrm{STATEMENT}-\mathrm{2}\::\:\mathrm{If}\:\mathrm{an}\:\mathrm{object}\:\mathrm{is}\:\mathrm{moving} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{friction}\:\mathrm{acting}\:\mathrm{on}\:\mathrm{it}\:\mathrm{has}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{kinetic}. \\ $$$$\mathrm{STATEMENT}-\mathrm{3}\::\:\mathrm{If}\:\mathrm{an}\:\mathrm{object}\:\mathrm{is}\:\mathrm{at}\:\mathrm{rest} \\ $$$$\mathrm{then}\:\mathrm{kinetic}\:\mathrm{friction}\:\mathrm{cannot}\:\mathrm{act}\:\mathrm{on}\:\mathrm{it}. \\ $$

Question Number 22059 Answers: 1 Comments: 0

A flywheel whose diameter is 1.5m decrease uniformly from 240rad/min until it came to rest 10s. Find the number of revolution made.

$$\mathrm{A}\:\mathrm{flywheel}\:\mathrm{whose}\:\mathrm{diameter}\:\mathrm{is}\:\mathrm{1}.\mathrm{5m}\:\mathrm{decrease}\:\mathrm{uniformly}\:\mathrm{from}\:\mathrm{240rad}/\mathrm{min} \\ $$$$\mathrm{until}\:\mathrm{it}\:\mathrm{came}\:\mathrm{to}\:\mathrm{rest}\:\mathrm{10s}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{revolution}\:\mathrm{made}. \\ $$

Question Number 22058 Answers: 1 Comments: 0

Two balls of mass 500g and 750g moving with 15m/s and 10m/s towards each other collides. Find the velocities of the ball after collision, if the coefficient of restitution is 0.8

$$\mathrm{Two}\:\mathrm{balls}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{500g}\:\mathrm{and}\:\mathrm{750g}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{15m}/\mathrm{s}\:\mathrm{and} \\ $$$$\mathrm{10m}/\mathrm{s}\:\mathrm{towards}\:\mathrm{each}\:\mathrm{other}\:\mathrm{collides}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{velocities}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{after} \\ $$$$\mathrm{collision},\:\mathrm{if}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{restitution}\:\mathrm{is}\:\mathrm{0}.\mathrm{8} \\ $$

Question Number 22052 Answers: 0 Comments: 2

A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the player is (a) frictional force along westward (b) muscle force along southward (c) frictional force along south-west (d) muscle force along south-west

$$\mathrm{A}\:\mathrm{hockey}\:\mathrm{player}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{northward} \\ $$$$\mathrm{and}\:\mathrm{suddenly}\:\mathrm{turns}\:\mathrm{westward}\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{speed}\:\mathrm{to}\:\mathrm{avoid}\:\mathrm{an}\:\mathrm{opponent}. \\ $$$$\mathrm{The}\:\mathrm{force}\:\mathrm{that}\:\mathrm{acts}\:\mathrm{on}\:\mathrm{the}\:\mathrm{player}\:\mathrm{is} \\ $$$$\left({a}\right)\:\mathrm{frictional}\:\mathrm{force}\:\mathrm{along}\:\mathrm{westward} \\ $$$$\left({b}\right)\:\mathrm{muscle}\:\mathrm{force}\:\mathrm{along}\:\mathrm{southward} \\ $$$$\left({c}\right)\:\mathrm{frictional}\:\mathrm{force}\:\mathrm{along}\:\mathrm{south}-\mathrm{west} \\ $$$$\left({d}\right)\:\mathrm{muscle}\:\mathrm{force}\:\mathrm{along}\:\mathrm{south}-\mathrm{west} \\ $$

Question Number 22050 Answers: 0 Comments: 0

Calculate the energy emitted when electrons of 1 g atom of hydrogen undergo transition giving the spectral line of lowest energy in the visible region of its atomic spectrum (R_H = 1.1 × 10^7 m^(−1) , c = 3 × 10^8 ms^(−1) , h = 6.62 × 10^(−34) Js)

$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{energy}\:\mathrm{emitted}\:\mathrm{when} \\ $$$$\mathrm{electrons}\:\mathrm{of}\:\mathrm{1}\:\mathrm{g}\:\mathrm{atom}\:\mathrm{of}\:\mathrm{hydrogen} \\ $$$$\mathrm{undergo}\:\mathrm{transition}\:\mathrm{giving}\:\mathrm{the}\:\mathrm{spectral} \\ $$$$\mathrm{line}\:\mathrm{of}\:\mathrm{lowest}\:\mathrm{energy}\:\mathrm{in}\:\mathrm{the}\:\mathrm{visible} \\ $$$$\mathrm{region}\:\mathrm{of}\:\mathrm{its}\:\mathrm{atomic}\:\mathrm{spectrum} \\ $$$$\left(\mathrm{R}_{\mathrm{H}} \:=\:\mathrm{1}.\mathrm{1}\:×\:\mathrm{10}^{\mathrm{7}} \:\mathrm{m}^{−\mathrm{1}} ,\:{c}\:=\:\mathrm{3}\:×\:\mathrm{10}^{\mathrm{8}} \:{ms}^{−\mathrm{1}} ,\right. \\ $$$$\left.{h}\:=\:\mathrm{6}.\mathrm{62}\:×\:\mathrm{10}^{−\mathrm{34}} \:\mathrm{Js}\right) \\ $$

Question Number 22020 Answers: 0 Comments: 0

The line of action of the resultant of two like parallel forces shifts by one fourth of the distance between the forces when the two forces are interchanged. The ratio of the two forces is

$$\mathrm{The}\:\mathrm{line}\:\mathrm{of}\:\mathrm{action}\:\mathrm{of}\:\mathrm{the}\:\mathrm{resultant}\:\mathrm{of} \\ $$$$\mathrm{two}\:\mathrm{like}\:\mathrm{parallel}\:\mathrm{forces}\:\mathrm{shifts}\:\mathrm{by}\:\mathrm{one} \\ $$$$\mathrm{fourth}\:\mathrm{of}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{forces}\:\mathrm{when}\:\mathrm{the}\:\mathrm{two}\:\mathrm{forces}\:\mathrm{are} \\ $$$$\mathrm{interchanged}.\:\mathrm{The}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{forces}\:\mathrm{is} \\ $$

Question Number 21967 Answers: 1 Comments: 1

A block is tied with a thread of length l and moved in a horizontal circle on a rough table. Coefficient of friction between block and table is μ = 0.2. Find tan θ, where θ is the angle between acceleration and frictional force at the instant when speed of particle is v = (√(1.6lg))

$$\mathrm{A}\:\mathrm{block}\:\mathrm{is}\:\mathrm{tied}\:\mathrm{with}\:\mathrm{a}\:\mathrm{thread}\:\mathrm{of}\:\mathrm{length}\:{l} \\ $$$$\mathrm{and}\:\mathrm{moved}\:\mathrm{in}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{circle}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{rough}\:\mathrm{table}.\:\mathrm{Coefficient}\:\mathrm{of}\:\mathrm{friction} \\ $$$$\mathrm{between}\:\mathrm{block}\:\mathrm{and}\:\mathrm{table}\:\mathrm{is}\:\mu\:=\:\mathrm{0}.\mathrm{2}. \\ $$$$\mathrm{Find}\:\mathrm{tan}\:\theta,\:\mathrm{where}\:\theta\:\mathrm{is}\:\mathrm{the}\:\mathrm{angle} \\ $$$$\mathrm{between}\:\mathrm{acceleration}\:\mathrm{and}\:\mathrm{frictional} \\ $$$$\mathrm{force}\:\mathrm{at}\:\mathrm{the}\:\mathrm{instant}\:\mathrm{when}\:\mathrm{speed}\:\mathrm{of} \\ $$$$\mathrm{particle}\:\mathrm{is}\:{v}\:=\:\sqrt{\mathrm{1}.\mathrm{6}{lg}} \\ $$

Question Number 21936 Answers: 1 Comments: 0

A heavy iron bar of weight W is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle θ with the horizontal. What is the weight experienced by the man?

$$\mathrm{A}\:\mathrm{heavy}\:\mathrm{iron}\:\mathrm{bar}\:\mathrm{of}\:\mathrm{weight}\:{W}\:\mathrm{is}\:\mathrm{having} \\ $$$$\mathrm{its}\:\mathrm{one}\:\mathrm{end}\:\mathrm{on}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{and}\:\mathrm{the}\:\mathrm{other} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{shoulder}\:\mathrm{of}\:\mathrm{a}\:\mathrm{man}.\:\mathrm{The}\:\mathrm{rod} \\ $$$$\mathrm{makes}\:\mathrm{an}\:\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the}\:\mathrm{horizontal}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{weight}\:\mathrm{experienced}\:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{man}? \\ $$

Question Number 21870 Answers: 1 Comments: 0

A wire of mass 9.8 × 10^(−3) kg per meter passes over a frictionless pulley fixed on the top of an inclined frictionless plane which makes an angle of 30° with the horizontal. Masses M_1 and M_2 are tied at the two ends of the wire. The mass M_1 rests on the plane and the mass M_2 hangs freely vertically downward. The whole system is in equilibrium. Now a transverse wave propagates along the wire with a velocity of 100 m/s. Find M_1 and M_2 (g = 9.8 m/s^2 ).

$$\mathrm{A}\:\mathrm{wire}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{9}.\mathrm{8}\:×\:\mathrm{10}^{−\mathrm{3}} \:\mathrm{kg}\:\mathrm{per}\:\mathrm{meter} \\ $$$$\mathrm{passes}\:\mathrm{over}\:\mathrm{a}\:\mathrm{frictionless}\:\mathrm{pulley}\:\mathrm{fixed} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{an}\:\mathrm{inclined}\:\mathrm{frictionless} \\ $$$$\mathrm{plane}\:\mathrm{which}\:\mathrm{makes}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{30}°\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{horizontal}.\:\mathrm{Masses}\:{M}_{\mathrm{1}} \:\mathrm{and}\:{M}_{\mathrm{2}} \:\mathrm{are} \\ $$$$\mathrm{tied}\:\mathrm{at}\:\mathrm{the}\:\mathrm{two}\:\mathrm{ends}\:\mathrm{of}\:\mathrm{the}\:\mathrm{wire}.\:\mathrm{The} \\ $$$$\mathrm{mass}\:{M}_{\mathrm{1}} \:\mathrm{rests}\:\mathrm{on}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{mass}\:{M}_{\mathrm{2}} \:\mathrm{hangs}\:\mathrm{freely}\:\mathrm{vertically} \\ $$$$\mathrm{downward}.\:\mathrm{The}\:\mathrm{whole}\:\mathrm{system}\:\mathrm{is}\:\mathrm{in} \\ $$$$\mathrm{equilibrium}.\:\mathrm{Now}\:\mathrm{a}\:\mathrm{transverse}\:\mathrm{wave} \\ $$$$\mathrm{propagates}\:\mathrm{along}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{velocity}\:\mathrm{of}\:\mathrm{100}\:\mathrm{m}/\mathrm{s}.\:\mathrm{Find}\:{M}_{\mathrm{1}} \:\mathrm{and}\:{M}_{\mathrm{2}} \\ $$$$\left({g}\:=\:\mathrm{9}.\mathrm{8}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \right). \\ $$

Question Number 21819 Answers: 0 Comments: 3

Consider the situation shown in figure in which a block P of mass 2 kg is placed over a block Q of mass 4 kg. The combination of the blocks are placed on inclined plane of inclination 37° with horizontal. The coefficient of friction between Block Q and inclined plane is μ_2 and in between the two blocks is μ_1 . The system is released from rest, then when will be the frictional force acting between the block is zero? (p) μ_1 = 0.4; μ_2 = 0 (q) μ_1 = 0.8; μ_2 = 0.8 (r) μ_1 = 0.4; μ_2 = 0.5 (s) μ_1 = 0.5; μ_2 = 0.4 (t) μ_1 = 0; μ_2 = 0.4

Question Number 21793 Answers: 0 Comments: 6

A plank of mass 10 kg rests on a smooth horizontal surface. Two blocks A and B of masses m_A = 2 kg and m_B = 1 kg lies at a distance of 3 m on the plank. The friction coefficient between the blocks and plank are μ_A = 0.3 and μ_B = 0.1. Now a force F = 15 N is applied to the plank in horizontal direction. Find the times (in sec) after which block A collides with B.

$$\mathrm{A}\:\mathrm{plank}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{10}\:\mathrm{kg}\:\mathrm{rests}\:\mathrm{on}\:\mathrm{a}\:\mathrm{smooth} \\ $$$$\mathrm{horizontal}\:\mathrm{surface}.\:\mathrm{Two}\:\mathrm{blocks}\:\mathrm{A}\:\mathrm{and} \\ $$$$\mathrm{B}\:\mathrm{of}\:\mathrm{masses}\:\mathrm{m}_{\mathrm{A}} \:=\:\mathrm{2}\:\mathrm{kg}\:\mathrm{and}\:\mathrm{m}_{\mathrm{B}} \:=\:\mathrm{1}\:\mathrm{kg} \\ $$$$\mathrm{lies}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{3}\:\mathrm{m}\:\mathrm{on}\:\mathrm{the}\:\mathrm{plank}. \\ $$$$\mathrm{The}\:\mathrm{friction}\:\mathrm{coefficient}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{blocks}\:\mathrm{and}\:\mathrm{plank}\:\mathrm{are}\:\mu_{\mathrm{A}} \:=\:\mathrm{0}.\mathrm{3}\:\mathrm{and}\:\mu_{\mathrm{B}} \:= \\ $$$$\mathrm{0}.\mathrm{1}.\:\mathrm{Now}\:\mathrm{a}\:\mathrm{force}\:\mathrm{F}\:=\:\mathrm{15}\:\mathrm{N}\:\mathrm{is}\:\mathrm{applied}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{plank}\:\mathrm{in}\:\mathrm{horizontal}\:\mathrm{direction}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{times}\:\left(\mathrm{in}\:\mathrm{sec}\right)\:\mathrm{after}\:\mathrm{which}\:\mathrm{block}\:\mathrm{A} \\ $$$$\mathrm{collides}\:\mathrm{with}\:\mathrm{B}. \\ $$

Question Number 24687 Answers: 1 Comments: 0

A particle starts from rest at t = 0 and moves with uniform acceleration. Then (1) In any time interval starting from t = 0 the space-average of the velocity is (4/3) times of time average velocity (2) If v = v_1 at t = t_1 and v = v_2 at t = t_2 then time average velocity between t_1 and t_2 is ((v_1 + v_2 )/2) (3) Distance travelled in successive equal time intervals are in proportion of 1 : 3 : 5 ... and so on (4) If v_1 , v_2 , v_3 denote the average velocities in three successive intervals of time t_1 , t_2 , t_3 then ((v_1 − v_2 )/(v_2 − v_3 )) = ((t_1 + t_2 )/(t_2 + t_3 ))

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{at}\:{t}\:=\:\mathrm{0}\:\mathrm{and} \\ $$$$\mathrm{moves}\:\mathrm{with}\:\mathrm{uniform}\:\mathrm{acceleration}.\:\mathrm{Then} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{In}\:\mathrm{any}\:\mathrm{time}\:\mathrm{interval}\:\mathrm{starting}\:\mathrm{from} \\ $$$${t}\:=\:\mathrm{0}\:\mathrm{the}\:\mathrm{space}-\mathrm{average}\:\mathrm{of}\:\mathrm{the}\:\mathrm{velocity} \\ $$$$\mathrm{is}\:\frac{\mathrm{4}}{\mathrm{3}}\:\mathrm{times}\:\mathrm{of}\:\mathrm{time}\:\mathrm{average}\:\mathrm{velocity} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{If}\:{v}\:=\:{v}_{\mathrm{1}} \:\mathrm{at}\:{t}\:=\:{t}_{\mathrm{1}} \:\mathrm{and}\:{v}\:=\:{v}_{\mathrm{2}} \:\mathrm{at}\:{t}\:=\:{t}_{\mathrm{2}} \\ $$$$\mathrm{then}\:\mathrm{time}\:\mathrm{average}\:\mathrm{velocity}\:\mathrm{between}\:{t}_{\mathrm{1}} \\ $$$$\mathrm{and}\:{t}_{\mathrm{2}} \:\mathrm{is}\:\frac{{v}_{\mathrm{1}} \:+\:{v}_{\mathrm{2}} }{\mathrm{2}} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Distance}\:\mathrm{travelled}\:\mathrm{in}\:\mathrm{successive} \\ $$$$\mathrm{equal}\:\mathrm{time}\:\mathrm{intervals}\:\mathrm{are}\:\mathrm{in}\:\mathrm{proportion} \\ $$$$\mathrm{of}\:\mathrm{1}\::\:\mathrm{3}\::\:\mathrm{5}\:...\:\mathrm{and}\:\mathrm{so}\:\mathrm{on} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{If}\:{v}_{\mathrm{1}} ,\:{v}_{\mathrm{2}} ,\:{v}_{\mathrm{3}} \:\mathrm{denote}\:\mathrm{the}\:\mathrm{average} \\ $$$$\mathrm{velocities}\:\mathrm{in}\:\mathrm{three}\:\mathrm{successive}\:\mathrm{intervals} \\ $$$$\mathrm{of}\:\mathrm{time}\:{t}_{\mathrm{1}} ,\:{t}_{\mathrm{2}} ,\:{t}_{\mathrm{3}} \:\mathrm{then}\:\frac{{v}_{\mathrm{1}} \:−\:{v}_{\mathrm{2}} }{{v}_{\mathrm{2}} \:−\:{v}_{\mathrm{3}} }\:=\:\frac{{t}_{\mathrm{1}} \:+\:{t}_{\mathrm{2}} }{{t}_{\mathrm{2}} \:+\:{t}_{\mathrm{3}} } \\ $$

Question Number 24685 Answers: 0 Comments: 3

The sum of the kinetic and potential energies of a system of objects is conserved (1) Only when no external force acts on the objects (2) Only when the objects move along closed paths (3) Only when the work done by the resultant external force is zero (4) None of these

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{kinetic}\:\mathrm{and}\:\mathrm{potential} \\ $$$$\mathrm{energies}\:\mathrm{of}\:\mathrm{a}\:\mathrm{system}\:\mathrm{of}\:\mathrm{objects}\:\mathrm{is}\:\mathrm{conserved} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Only}\:\mathrm{when}\:\mathrm{no}\:\mathrm{external}\:\mathrm{force}\:\mathrm{acts}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{objects} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Only}\:\mathrm{when}\:\mathrm{the}\:\mathrm{objects}\:\mathrm{move}\:\mathrm{along} \\ $$$$\mathrm{closed}\:\mathrm{paths} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Only}\:\mathrm{when}\:\mathrm{the}\:\mathrm{work}\:\mathrm{done}\:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{resultant}\:\mathrm{external}\:\mathrm{force}\:\mathrm{is}\:\mathrm{zero} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{None}\:\mathrm{of}\:\mathrm{these} \\ $$

Question Number 21759 Answers: 1 Comments: 0

A block of mass 1 kg is pushed against a rough vertical wall with a force of 20 N, coefficient of static friction being (1/4). Another horizontal force of 10 N is applied on the block in a direction parallel to the wall. Will the block move? If yes, with what acceleration? If no, find the frictional force exerted by wall on the block. (g = 10 m/s^2 )

$$\mathrm{A}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{pushed}\:\mathrm{against} \\ $$$$\mathrm{a}\:\mathrm{rough}\:\mathrm{vertical}\:\mathrm{wall}\:\mathrm{with}\:\mathrm{a}\:\mathrm{force}\:\mathrm{of}\:\mathrm{20} \\ $$$$\mathrm{N},\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{static}\:\mathrm{friction}\:\mathrm{being}\:\frac{\mathrm{1}}{\mathrm{4}}. \\ $$$$\mathrm{Another}\:\mathrm{horizontal}\:\mathrm{force}\:\mathrm{of}\:\mathrm{10}\:\mathrm{N}\:\mathrm{is} \\ $$$$\mathrm{applied}\:\mathrm{on}\:\mathrm{the}\:\mathrm{block}\:\mathrm{in}\:\mathrm{a}\:\mathrm{direction} \\ $$$$\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{wall}.\:\mathrm{Will}\:\mathrm{the}\:\mathrm{block}\:\mathrm{move}? \\ $$$$\mathrm{If}\:\mathrm{yes},\:\mathrm{with}\:\mathrm{what}\:\mathrm{acceleration}?\:\mathrm{If}\:\mathrm{no}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{frictional}\:\mathrm{force}\:\mathrm{exerted}\:\mathrm{by}\:\mathrm{wall} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{block}.\:\left({g}\:=\:\mathrm{10}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \right) \\ $$

Question Number 21750 Answers: 0 Comments: 2

Column II gives five arrangements of two blocks A and B. In each arrangement their masses are 3 kg and 2 kg respectively. Match the entries in column I with arrangements in column II. Column I (A) Force on B w.r.t. A is equal to force on A w.r.t. B (B) Net force on B w.r.t. an inertial frame is 4 N (C) Acceleration of the block A is 2 m/s^2 . (D) Net force on B w.r.t. A is 8 N

$$\mathrm{Column}\:\mathrm{II}\:\mathrm{gives}\:\mathrm{five}\:\mathrm{arrangements}\:\mathrm{of} \\ $$$$\mathrm{two}\:\mathrm{blocks}\:{A}\:\mathrm{and}\:{B}.\:\mathrm{In}\:\mathrm{each} \\ $$$$\mathrm{arrangement}\:\mathrm{their}\:\mathrm{masses}\:\mathrm{are}\:\mathrm{3}\:\mathrm{kg}\:\mathrm{and} \\ $$$$\mathrm{2}\:\mathrm{kg}\:\mathrm{respectively}.\:\mathrm{Match}\:\mathrm{the}\:\mathrm{entries}\:\mathrm{in} \\ $$$$\mathrm{column}\:\mathrm{I}\:\mathrm{with}\:\mathrm{arrangements}\:\mathrm{in}\:\mathrm{column} \\ $$$$\mathrm{II}. \\ $$$$\boldsymbol{\mathrm{Column}}\:\boldsymbol{\mathrm{I}} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{Force}\:\mathrm{on}\:{B}\:\mathrm{w}.\mathrm{r}.\mathrm{t}.\:{A}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{force} \\ $$$$\mathrm{on}\:{A}\:\mathrm{w}.\mathrm{r}.\mathrm{t}.\:{B} \\ $$$$\left(\mathrm{B}\right)\:\mathrm{Net}\:\mathrm{force}\:\mathrm{on}\:{B}\:\mathrm{w}.\mathrm{r}.\mathrm{t}.\:\mathrm{an}\:\mathrm{inertial} \\ $$$$\mathrm{frame}\:\mathrm{is}\:\mathrm{4}\:\mathrm{N} \\ $$$$\left(\mathrm{C}\right)\:\mathrm{Acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{block}\:{A}\:\mathrm{is}\:\mathrm{2} \\ $$$$\mathrm{m}/\mathrm{s}^{\mathrm{2}} . \\ $$$$\left(\mathrm{D}\right)\:\mathrm{Net}\:\mathrm{force}\:\mathrm{on}\:{B}\:\mathrm{w}.\mathrm{r}.\mathrm{t}.\:{A}\:\mathrm{is}\:\mathrm{8}\:\mathrm{N} \\ $$

Question Number 21747 Answers: 0 Comments: 4

Three blocks of masses m_1 , m_2 and m_3 are connected as shown. All the surfaces are frictionless and the string and the pulleys are light. Find the acceleration of m_1 .

$$\mathrm{Three}\:\mathrm{blocks}\:\mathrm{of}\:\mathrm{masses}\:{m}_{\mathrm{1}} ,\:{m}_{\mathrm{2}} \:\mathrm{and}\:{m}_{\mathrm{3}} \\ $$$$\mathrm{are}\:\mathrm{connected}\:\mathrm{as}\:\mathrm{shown}.\:\mathrm{All}\:\mathrm{the}\:\mathrm{surfaces} \\ $$$$\mathrm{are}\:\mathrm{frictionless}\:\mathrm{and}\:\mathrm{the}\:\mathrm{string}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{pulleys}\:\mathrm{are}\:\mathrm{light}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:{m}_{\mathrm{1}} . \\ $$

Question Number 21731 Answers: 0 Comments: 0

A very flexible uniform chain of mass M and length L is suspended vertically so that its lower end just touches the surface of a table. When the upper end of the chain is released, it falls with each link coming to rest the instant it strikes the table. Find the force exerted by the chain on the table at the moment when x part of chain has already rested on the table.

Question Number 21713 Answers: 0 Comments: 7

A constant force F = 20 N acts on a block of mass 2 kg which is connected to two blocks of masses m_1 = 1 kg and m_2 = 2 kg. Calculate the accelerations produced in all the three blocks. Assume pulleys are frictionless and weightless.

$$\mathrm{A}\:\mathrm{constant}\:\mathrm{force}\:{F}\:=\:\mathrm{20}\:\mathrm{N}\:\mathrm{acts}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2}\:\mathrm{kg}\:\mathrm{which}\:\mathrm{is}\:\mathrm{connected}\:\mathrm{to} \\ $$$$\mathrm{two}\:\mathrm{blocks}\:\mathrm{of}\:\mathrm{masses}\:{m}_{\mathrm{1}} \:=\:\mathrm{1}\:\mathrm{kg}\:\mathrm{and} \\ $$$${m}_{\mathrm{2}} \:=\:\mathrm{2}\:\mathrm{kg}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{accelerations} \\ $$$$\mathrm{produced}\:\mathrm{in}\:\mathrm{all}\:\mathrm{the}\:\mathrm{three}\:\mathrm{blocks}.\:\mathrm{Assume} \\ $$$$\mathrm{pulleys}\:\mathrm{are}\:\mathrm{frictionless}\:\mathrm{and}\:\mathrm{weightless}. \\ $$

Question Number 21670 Answers: 1 Comments: 1

The block of mass 2 kg and 3 kg are placed one over the other. The contact surfaces are rough with coefficient of friction μ_1 = 0.2, μ_2 = 0.06. A force F = (1/2)t N (where t is in second) is applied on upper block in the direction. (Given that g = 10 m/s^2 ) 1. The relative slipping between the blocks occurs at t = 2. Friction force acting between the two blocks at t = 8 s 3. The acceleration time graph for 3 kg block is

$$\mathrm{The}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2}\:\mathrm{kg}\:\mathrm{and}\:\mathrm{3}\:\mathrm{kg}\:\mathrm{are} \\ $$$$\mathrm{placed}\:\mathrm{one}\:\mathrm{over}\:\mathrm{the}\:\mathrm{other}.\:\mathrm{The}\:\mathrm{contact} \\ $$$$\mathrm{surfaces}\:\mathrm{are}\:\mathrm{rough}\:\mathrm{with}\:\mathrm{coefficient}\:\mathrm{of} \\ $$$$\mathrm{friction}\:\mu_{\mathrm{1}} \:=\:\mathrm{0}.\mathrm{2},\:\mu_{\mathrm{2}} \:=\:\mathrm{0}.\mathrm{06}.\:\mathrm{A}\:\mathrm{force}\:{F}\:= \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{t}\:\mathrm{N}\:\left(\mathrm{where}\:{t}\:\mathrm{is}\:\mathrm{in}\:\mathrm{second}\right)\:\mathrm{is}\:\mathrm{applied} \\ $$$$\mathrm{on}\:\mathrm{upper}\:\mathrm{block}\:\mathrm{in}\:\mathrm{the}\:\mathrm{direction}.\:\left(\mathrm{Given}\right. \\ $$$$\left.\mathrm{that}\:{g}\:=\:\mathrm{10}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \right) \\ $$$$\mathrm{1}.\:\mathrm{The}\:\mathrm{relative}\:\mathrm{slipping}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{blocks}\:\mathrm{occurs}\:\mathrm{at}\:{t}\:= \\ $$$$\mathrm{2}.\:\mathrm{Friction}\:\mathrm{force}\:\mathrm{acting}\:\mathrm{between}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{blocks}\:\mathrm{at}\:{t}\:=\:\mathrm{8}\:\mathrm{s} \\ $$$$\mathrm{3}.\:\mathrm{The}\:\mathrm{acceleration}\:\mathrm{time}\:\mathrm{graph}\:\mathrm{for}\:\mathrm{3}\:\mathrm{kg} \\ $$$$\mathrm{block}\:\mathrm{is} \\ $$

Question Number 21661 Answers: 0 Comments: 2

Question Number 21628 Answers: 1 Comments: 0

One end of a massless spring of constant 100 N/m and natural length 0.5 m is fixed and the other end is connected to a particle of mass 0.5 kg lying on a frictionless horizontal table. The spring remains horizontal. If the mass is made to rotate at an angular velocity of 2 rad/s, find the elongation of the spring.

$$\mathrm{One}\:\mathrm{end}\:\mathrm{of}\:\mathrm{a}\:\mathrm{massless}\:\mathrm{spring}\:\mathrm{of}\:\mathrm{constant} \\ $$$$\mathrm{100}\:\mathrm{N}/\mathrm{m}\:\mathrm{and}\:\mathrm{natural}\:\mathrm{length}\:\mathrm{0}.\mathrm{5}\:\mathrm{m}\:\mathrm{is} \\ $$$$\mathrm{fixed}\:\mathrm{and}\:\mathrm{the}\:\mathrm{other}\:\mathrm{end}\:\mathrm{is}\:\mathrm{connected}\:\mathrm{to} \\ $$$$\mathrm{a}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{0}.\mathrm{5}\:\mathrm{kg}\:\mathrm{lying}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{frictionless}\:\mathrm{horizontal}\:\mathrm{table}.\:\mathrm{The}\:\mathrm{spring} \\ $$$$\mathrm{remains}\:\mathrm{horizontal}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{mass}\:\mathrm{is}\:\mathrm{made} \\ $$$$\mathrm{to}\:\mathrm{rotate}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angular}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{2} \\ $$$$\mathrm{rad}/{s},\:\mathrm{find}\:\mathrm{the}\:\mathrm{elongation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{spring}. \\ $$

Question Number 21626 Answers: 0 Comments: 1

Is it also possible to import text or fomulars from other apps using the android−clipboard?

$$\mathrm{Is}\:\mathrm{it}\:\mathrm{also}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{import}\:\mathrm{text}\:\mathrm{or}\:\mathrm{fomulars} \\ $$$$\mathrm{from}\:\mathrm{other}\:\mathrm{apps}\:\mathrm{using}\:\mathrm{the}\:\mathrm{android}−\mathrm{clipboard}? \\ $$

Question Number 21604 Answers: 1 Comments: 0

A particle will leave a vertical circle of radius r, when its velocity at the lowest point of the circle (v_L ) is (a) (√(2gr)) (b) (√(5gr)) (c) (√(3gr)) (d) (√(6gr))

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{will}\:\mathrm{leave}\:\mathrm{a}\:\mathrm{vertical}\:\mathrm{circle}\:\mathrm{of} \\ $$$$\mathrm{radius}\:{r},\:\mathrm{when}\:\mathrm{its}\:\mathrm{velocity}\:\mathrm{at}\:\mathrm{the}\:\mathrm{lowest} \\ $$$$\mathrm{point}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\left({v}_{{L}} \right)\:\mathrm{is} \\ $$$$\left({a}\right)\:\sqrt{\mathrm{2}{gr}} \\ $$$$\left({b}\right)\:\sqrt{\mathrm{5}{gr}} \\ $$$$\left({c}\right)\:\sqrt{\mathrm{3}{gr}} \\ $$$$\left({d}\right)\:\sqrt{\mathrm{6}{gr}} \\ $$

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