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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))

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

Question Number 21580    Answers: 1   Comments: 0

Question Number 21564    Answers: 0   Comments: 1

A block of mass M is placed on smooth ground. Its upper surface is smooth and vertical surface is rough with coefficient of friction μ. A block of mass m_1 is placed on its horizontal surface and tied with a massless inextensible string passing over smooth pulley. Its other end is connected to another block of mass m_2 , which touches the vertical surface of block M. Now a horizontal force F starts acting on it. Q1. Which of the following is incorrect about above system? (1) There exists a value of F at which friction force is equal to zero (2) When F = 0, the blocks cannot remain stationary (3) There exists two limiting values of F at which the blocks m_1 and m_2 will remain stationary w.r.t. block of mass M (4) The limiting friction between m_2 and M is independent of F Q2. In the above case, let m_1 − μm_2 be greater than 1. Choose the incorrect value of F for which the blocks m_1 and m_2 remain stationary with respect to M (1) (M + m_1 + m_2 )((m_2 g)/m_1 ) (2) ((m_2 (M + m_1 + m_2 ))/((m_1 − μm_2 )))g (3) (((M + m_1 + m_2 )m_2 g)/((m_1 + μm_2 ))) (4) (M + m_1 + m_2 )(g/μ) Q3. Let vertical part of block M be smooth. Choose the correct alternative (1) There exist two limiting values for system to remain relatively at rest (2) For one unique value of F, the blocks m_1 and m_2 remain stationary with respect to block M (3) The blocks m_1 and m_2 cannot be in equilibrium for any value of F (4) There exists a range of mass M, for which system remains stationary

$$\mathrm{A}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:{M}\:\mathrm{is}\:\mathrm{placed}\:\mathrm{on}\:\mathrm{smooth} \\ $$$$\mathrm{ground}.\:\mathrm{Its}\:\mathrm{upper}\:\mathrm{surface}\:\mathrm{is}\:\mathrm{smooth}\:\mathrm{and} \\ $$$$\mathrm{vertical}\:\mathrm{surface}\:\mathrm{is}\:\mathrm{rough}\:\mathrm{with}\:\mathrm{coefficient} \\ $$$$\mathrm{of}\:\mathrm{friction}\:\mu.\:\mathrm{A}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:{m}_{\mathrm{1}} \:\mathrm{is}\:\mathrm{placed} \\ $$$$\mathrm{on}\:\mathrm{its}\:\mathrm{horizontal}\:\mathrm{surface}\:\mathrm{and}\:\mathrm{tied}\:\mathrm{with} \\ $$$$\mathrm{a}\:\mathrm{massless}\:\mathrm{inextensible}\:\mathrm{string}\:\mathrm{passing} \\ $$$$\mathrm{over}\:\mathrm{smooth}\:\mathrm{pulley}.\:\mathrm{Its}\:\mathrm{other}\:\mathrm{end}\:\mathrm{is} \\ $$$$\mathrm{connected}\:\mathrm{to}\:\mathrm{another}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:{m}_{\mathrm{2}} , \\ $$$$\mathrm{which}\:\mathrm{touches}\:\mathrm{the}\:\mathrm{vertical}\:\mathrm{surface}\:\mathrm{of} \\ $$$$\mathrm{block}\:{M}.\:\mathrm{Now}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{force}\:{F} \\ $$$$\mathrm{starts}\:\mathrm{acting}\:\mathrm{on}\:\mathrm{it}. \\ $$$$\boldsymbol{\mathrm{Q}}\mathrm{1}.\:\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{incorrect} \\ $$$$\mathrm{about}\:\mathrm{above}\:\mathrm{system}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{There}\:\mathrm{exists}\:\mathrm{a}\:\mathrm{value}\:\mathrm{of}\:{F}\:\mathrm{at}\:\mathrm{which} \\ $$$$\mathrm{friction}\:\mathrm{force}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{zero} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{When}\:{F}\:=\:\mathrm{0},\:\mathrm{the}\:\mathrm{blocks}\:\mathrm{cannot} \\ $$$$\mathrm{remain}\:\mathrm{stationary} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{There}\:\mathrm{exists}\:\mathrm{two}\:\mathrm{limiting}\:\mathrm{values}\:\mathrm{of} \\ $$$${F}\:\mathrm{at}\:\mathrm{which}\:\mathrm{the}\:\mathrm{blocks}\:{m}_{\mathrm{1}} \:\mathrm{and}\:{m}_{\mathrm{2}} \:\mathrm{will} \\ $$$$\mathrm{remain}\:\mathrm{stationary}\:\mathrm{w}.\mathrm{r}.\mathrm{t}.\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass} \\ $$$${M} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{The}\:\mathrm{limiting}\:\mathrm{friction}\:\mathrm{between}\:{m}_{\mathrm{2}} \\ $$$$\mathrm{and}\:{M}\:\mathrm{is}\:\mathrm{independent}\:\mathrm{of}\:{F} \\ $$$$\boldsymbol{\mathrm{Q}}\mathrm{2}.\:\mathrm{In}\:\mathrm{the}\:\mathrm{above}\:\mathrm{case},\:\mathrm{let}\:{m}_{\mathrm{1}} \:−\:\mu{m}_{\mathrm{2}} \:\mathrm{be} \\ $$$$\mathrm{greater}\:\mathrm{than}\:\mathrm{1}.\:\mathrm{Choose}\:\mathrm{the}\:\mathrm{incorrect} \\ $$$$\mathrm{value}\:\mathrm{of}\:{F}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{blocks}\:{m}_{\mathrm{1}} \:\mathrm{and} \\ $$$${m}_{\mathrm{2}} \:\mathrm{remain}\:\mathrm{stationary}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to} \\ $$$${M} \\ $$$$\left(\mathrm{1}\right)\:\left({M}\:+\:{m}_{\mathrm{1}} \:+\:{m}_{\mathrm{2}} \right)\frac{{m}_{\mathrm{2}} {g}}{{m}_{\mathrm{1}} } \\ $$$$\left(\mathrm{2}\right)\:\frac{{m}_{\mathrm{2}} \left({M}\:+\:{m}_{\mathrm{1}} \:+\:{m}_{\mathrm{2}} \right)}{\left({m}_{\mathrm{1}} \:−\:\mu{m}_{\mathrm{2}} \right)}{g} \\ $$$$\left(\mathrm{3}\right)\:\frac{\left({M}\:+\:{m}_{\mathrm{1}} \:+\:{m}_{\mathrm{2}} \right){m}_{\mathrm{2}} {g}}{\left({m}_{\mathrm{1}} \:+\:\mu{m}_{\mathrm{2}} \right)} \\ $$$$\left(\mathrm{4}\right)\:\left({M}\:+\:{m}_{\mathrm{1}} \:+\:{m}_{\mathrm{2}} \right)\frac{{g}}{\mu} \\ $$$$\boldsymbol{\mathrm{Q}}\mathrm{3}.\:\mathrm{Let}\:\mathrm{vertical}\:\mathrm{part}\:\mathrm{of}\:\mathrm{block}\:{M}\:\mathrm{be} \\ $$$$\mathrm{smooth}.\:\mathrm{Choose}\:\mathrm{the}\:\mathrm{correct}\:\mathrm{alternative} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{There}\:\mathrm{exist}\:\mathrm{two}\:\mathrm{limiting}\:\mathrm{values}\:\mathrm{for} \\ $$$$\mathrm{system}\:\mathrm{to}\:\mathrm{remain}\:\mathrm{relatively}\:\mathrm{at}\:\mathrm{rest} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{For}\:\mathrm{one}\:\mathrm{unique}\:\mathrm{value}\:\mathrm{of}\:{F},\:\mathrm{the}\:\mathrm{blocks} \\ $$$${m}_{\mathrm{1}} \:\mathrm{and}\:{m}_{\mathrm{2}} \:\mathrm{remain}\:\mathrm{stationary}\:\mathrm{with} \\ $$$$\mathrm{respect}\:\mathrm{to}\:\mathrm{block}\:{M} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{The}\:\mathrm{blocks}\:{m}_{\mathrm{1}} \:\mathrm{and}\:{m}_{\mathrm{2}} \:\mathrm{cannot}\:\mathrm{be}\:\mathrm{in} \\ $$$$\mathrm{equilibrium}\:\mathrm{for}\:\mathrm{any}\:\mathrm{value}\:\mathrm{of}\:{F} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{There}\:\mathrm{exists}\:\mathrm{a}\:\mathrm{range}\:\mathrm{of}\:\mathrm{mass}\:{M},\:\mathrm{for} \\ $$$$\mathrm{which}\:\mathrm{system}\:\mathrm{remains}\:\mathrm{stationary} \\ $$

Question Number 21557    Answers: 0   Comments: 0

A man of mass 85 kg stands on a lift of mass 30 kg. When he pulls on the rope, he exerts a force of 400 N on the floor of the lift. Calculate acceleration of the lift. Given g = 10 m/s^2 .

$$\mathrm{A}\:\mathrm{man}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{85}\:\mathrm{kg}\:\mathrm{stands}\:\mathrm{on}\:\mathrm{a}\:\mathrm{lift}\:\mathrm{of} \\ $$$$\mathrm{mass}\:\mathrm{30}\:\mathrm{kg}.\:\mathrm{When}\:\mathrm{he}\:\mathrm{pulls}\:\mathrm{on}\:\mathrm{the}\:\mathrm{rope}, \\ $$$$\mathrm{he}\:\mathrm{exerts}\:\mathrm{a}\:\mathrm{force}\:\mathrm{of}\:\mathrm{400}\:\mathrm{N}\:\mathrm{on}\:\mathrm{the}\:\mathrm{floor}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{lift}.\:\mathrm{Calculate}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{lift}.\:\mathrm{Given}\:{g}\:=\:\mathrm{10}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} . \\ $$

Question Number 21545    Answers: 0   Comments: 0

Question Number 21535    Answers: 0   Comments: 0

Which forces of attraction are responsible for liquefaction of H_2 ? (a) Coulombic forces (b) Dipole forces (c) Hydrogen bonding (d) Van der Waal′s forces.

$$\mathrm{Which}\:\mathrm{forces}\:\mathrm{of}\:\mathrm{attraction}\:\mathrm{are}\:\mathrm{responsible} \\ $$$$\mathrm{for}\:\mathrm{liquefaction}\:\mathrm{of}\:\mathrm{H}_{\mathrm{2}} ? \\ $$$$\left({a}\right)\:\mathrm{Coulombic}\:\mathrm{forces} \\ $$$$\left({b}\right)\:\mathrm{Dipole}\:\mathrm{forces} \\ $$$$\left({c}\right)\:\mathrm{Hydrogen}\:\mathrm{bonding} \\ $$$$\left({d}\right)\:\mathrm{Van}\:\mathrm{der}\:\mathrm{Waal}'\mathrm{s}\:\mathrm{forces}. \\ $$

Question Number 21516    Answers: 2   Comments: 0

A 5-kg body is suspended from a spring- balance, and an identical body is balanced on a pan of a physical balance. If both the balances are kept in an elevator, then what would happen in each case when the elevator is moving with an upward acceleration?

$$\mathrm{A}\:\mathrm{5}-\mathrm{kg}\:\mathrm{body}\:\mathrm{is}\:\mathrm{suspended}\:\mathrm{from}\:\mathrm{a}\:\mathrm{spring}- \\ $$$$\mathrm{balance},\:\mathrm{and}\:\mathrm{an}\:\mathrm{identical}\:\mathrm{body}\:\mathrm{is} \\ $$$$\mathrm{balanced}\:\mathrm{on}\:\mathrm{a}\:\mathrm{pan}\:\mathrm{of}\:\mathrm{a}\:\mathrm{physical} \\ $$$$\mathrm{balance}.\:\mathrm{If}\:\mathrm{both}\:\mathrm{the}\:\mathrm{balances}\:\mathrm{are}\:\mathrm{kept} \\ $$$$\mathrm{in}\:\mathrm{an}\:\mathrm{elevator},\:\mathrm{then}\:\mathrm{what}\:\mathrm{would}\:\mathrm{happen} \\ $$$$\mathrm{in}\:\mathrm{each}\:\mathrm{case}\:\mathrm{when}\:\mathrm{the}\:\mathrm{elevator}\:\mathrm{is}\:\mathrm{moving} \\ $$$$\mathrm{with}\:\mathrm{an}\:\mathrm{upward}\:\mathrm{acceleration}? \\ $$

Question Number 21486    Answers: 0   Comments: 0

Vapour pressure in a closed container can be changed by (1) Adding water vapours from outside at same temperature (2) Adding ice at same temperature (3) Adding water at same temperature (4) Increasing temperature

$$\mathrm{Vapour}\:\mathrm{pressure}\:\mathrm{in}\:\mathrm{a}\:\mathrm{closed}\:\mathrm{container} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{changed}\:\mathrm{by} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Adding}\:\mathrm{water}\:\mathrm{vapours}\:\mathrm{from}\:\mathrm{outside} \\ $$$$\mathrm{at}\:\mathrm{same}\:\mathrm{temperature} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Adding}\:\mathrm{ice}\:\mathrm{at}\:\mathrm{same}\:\mathrm{temperature} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Adding}\:\mathrm{water}\:\mathrm{at}\:\mathrm{same}\:\mathrm{temperature} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Increasing}\:\mathrm{temperature} \\ $$

Question Number 21484    Answers: 0   Comments: 0

Positive deviation from ideal behaviour takes place because of (a) molecular interaction between atoms and PV/nRT > 1 (b) molecular interaction between atoms and PV/nRT < 1 (c) finite size of the atoms and PV/nRT > 1 (d) finite size of the atoms and PV/nRT < 1

$$\mathrm{Positive}\:\mathrm{deviation}\:\mathrm{from}\:\mathrm{ideal}\:\mathrm{behaviour} \\ $$$$\mathrm{takes}\:\mathrm{place}\:\mathrm{because}\:\mathrm{of} \\ $$$$\left({a}\right)\:\mathrm{molecular}\:\mathrm{interaction}\:\mathrm{between} \\ $$$$\mathrm{atoms}\:\mathrm{and}\:\mathrm{PV}/{n}\mathrm{RT}\:>\:\mathrm{1} \\ $$$$\left({b}\right)\:\mathrm{molecular}\:\mathrm{interaction}\:\mathrm{between} \\ $$$$\mathrm{atoms}\:\mathrm{and}\:\mathrm{PV}/{n}\mathrm{RT}\:<\:\mathrm{1} \\ $$$$\left({c}\right)\:\mathrm{finite}\:\mathrm{size}\:\mathrm{of}\:\mathrm{the}\:\mathrm{atoms}\:\mathrm{and}\:\mathrm{PV}/{n}\mathrm{RT}\:>\:\mathrm{1} \\ $$$$\left({d}\right)\:\mathrm{finite}\:\mathrm{size}\:\mathrm{of}\:\mathrm{the}\:\mathrm{atoms}\:\mathrm{and}\:\mathrm{PV}/{n}\mathrm{RT}\:<\:\mathrm{1} \\ $$

Question Number 21482    Answers: 0   Comments: 0

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Question Number 21469    Answers: 1   Comments: 1

Three identical blocks, each having a mass M, are pushed by a force F on a frictionless table. What is the net force on the block A?

$$\mathrm{Three}\:\mathrm{identical}\:\mathrm{blocks},\:\mathrm{each}\:\mathrm{having}\:\mathrm{a} \\ $$$$\mathrm{mass}\:{M},\:\mathrm{are}\:\mathrm{pushed}\:\mathrm{by}\:\mathrm{a}\:\mathrm{force}\:{F}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{frictionless}\:\mathrm{table}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{net}\:\mathrm{force} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{block}\:{A}? \\ $$

Question Number 21507    Answers: 1   Comments: 1

The length of an ideal spring increases by 0.1 cm when a body of 1 kg is suspended from it. If this spring is laid on a frictionless horizontal table and bodies of 1 kg each are suspended from its ends, then what will be the increase in its length?

$$\mathrm{The}\:\mathrm{length}\:\mathrm{of}\:\mathrm{an}\:\mathrm{ideal}\:\mathrm{spring}\:\mathrm{increases} \\ $$$$\mathrm{by}\:\mathrm{0}.\mathrm{1}\:\mathrm{cm}\:\mathrm{when}\:\mathrm{a}\:\mathrm{body}\:\mathrm{of}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{is} \\ $$$$\mathrm{suspended}\:\mathrm{from}\:\mathrm{it}.\:\mathrm{If}\:\mathrm{this}\:\mathrm{spring}\:\mathrm{is}\:\mathrm{laid} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{frictionless}\:\mathrm{horizontal}\:\mathrm{table}\:\mathrm{and} \\ $$$$\mathrm{bodies}\:\mathrm{of}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{each}\:\mathrm{are}\:\mathrm{suspended}\:\mathrm{from} \\ $$$$\mathrm{its}\:\mathrm{ends},\:\mathrm{then}\:\mathrm{what}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{increase} \\ $$$$\mathrm{in}\:\mathrm{its}\:\mathrm{length}? \\ $$

Question Number 21441    Answers: 1   Comments: 0

Find α in terms of θ using the equations: (i) u^2 sin^2 α = 2gd cos θ (ii) t = ((u cos α)/(g sin θ)) (iii) −d = ut sin α − ((gt^2 sin θ)/2)

$$\mathrm{Find}\:\alpha\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\theta\:\mathrm{using}\:\mathrm{the}\:\mathrm{equations}: \\ $$$$\left({i}\right)\:{u}^{\mathrm{2}} \:\mathrm{sin}^{\mathrm{2}} \:\alpha\:=\:\mathrm{2}{gd}\:\mathrm{cos}\:\theta \\ $$$$\left({ii}\right)\:{t}\:=\:\frac{{u}\:\mathrm{cos}\:\alpha}{{g}\:\mathrm{sin}\:\theta} \\ $$$$\left({iii}\right)\:−{d}\:=\:{ut}\:\mathrm{sin}\:\alpha\:−\:\frac{{gt}^{\mathrm{2}} \:\mathrm{sin}\:\theta}{\mathrm{2}} \\ $$

Question Number 21412    Answers: 0   Comments: 0

The atomic masses of ′He′ and ′Ne′ are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength of ′He′ gas at −73°C is “M” times that of the de Broglie wavelength of ′Ne′ at 727°C ′M′ is

$$\mathrm{The}\:\mathrm{atomic}\:\mathrm{masses}\:\mathrm{of}\:'\mathrm{He}'\:\mathrm{and}\:'\mathrm{Ne}'\:\mathrm{are} \\ $$$$\mathrm{4}\:\mathrm{and}\:\mathrm{20}\:\mathrm{a}.\mathrm{m}.\mathrm{u}.,\:\mathrm{respectively}.\:\mathrm{The} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{de}\:\mathrm{Broglie}\:\mathrm{wavelength}\:\mathrm{of} \\ $$$$'\mathrm{He}'\:\mathrm{gas}\:\mathrm{at}\:−\mathrm{73}°\mathrm{C}\:\mathrm{is}\:``\mathrm{M}''\:\mathrm{times}\:\mathrm{that}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{de}\:\mathrm{Broglie}\:\mathrm{wavelength}\:\mathrm{of}\:'\mathrm{Ne}'\:\mathrm{at} \\ $$$$\mathrm{727}°\mathrm{C}\:'\mathrm{M}'\:\mathrm{is} \\ $$

Question Number 21411    Answers: 0   Comments: 0

The critical temperature of water is higher than that of O_2 because the H_2 O molecule has (a) fewer electrons than O_2 (b) two covalent bonds (c) V-shape (d) dipole moment.

$$\mathrm{The}\:\mathrm{critical}\:\mathrm{temperature}\:\mathrm{of}\:\mathrm{water}\:\mathrm{is} \\ $$$$\mathrm{higher}\:\mathrm{than}\:\mathrm{that}\:\mathrm{of}\:\mathrm{O}_{\mathrm{2}} \:\mathrm{because}\:\mathrm{the} \\ $$$$\mathrm{H}_{\mathrm{2}} \mathrm{O}\:\mathrm{molecule}\:\mathrm{has} \\ $$$$\left({a}\right)\:\mathrm{fewer}\:\mathrm{electrons}\:\mathrm{than}\:\mathrm{O}_{\mathrm{2}} \\ $$$$\left({b}\right)\:\mathrm{two}\:\mathrm{covalent}\:\mathrm{bonds} \\ $$$$\left({c}\right)\:\mathrm{V}-\mathrm{shape} \\ $$$$\left({d}\right)\:\mathrm{dipole}\:\mathrm{moment}. \\ $$

Question Number 21388    Answers: 0   Comments: 4

A block of mass m is connected with another block of mass 2m by a light spring. 2m is connected with a hanging mass 3m by an inextensible light string. At the time of release of block 3m, find tension in the string and acceleration of all the masses.

$$\mathrm{A}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{is}\:\mathrm{connected}\:\mathrm{with} \\ $$$$\mathrm{another}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2}{m}\:\mathrm{by}\:\mathrm{a}\:\mathrm{light} \\ $$$$\mathrm{spring}.\:\mathrm{2}{m}\:\mathrm{is}\:\mathrm{connected}\:\mathrm{with}\:\mathrm{a}\:\mathrm{hanging} \\ $$$$\mathrm{mass}\:\mathrm{3}{m}\:\mathrm{by}\:\mathrm{an}\:\mathrm{inextensible}\:\mathrm{light}\:\mathrm{string}. \\ $$$$\mathrm{At}\:\mathrm{the}\:\mathrm{time}\:\mathrm{of}\:\mathrm{release}\:\mathrm{of}\:\mathrm{block}\:\mathrm{3}{m},\:\mathrm{find} \\ $$$$\mathrm{tension}\:\mathrm{in}\:\mathrm{the}\:\mathrm{string}\:\mathrm{and}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{masses}. \\ $$

Question Number 21377    Answers: 0   Comments: 0

Balls are dropped from the roof of a tower at a fixed interval of time. At the moment when 9th ball reaches the ground the nth ball is (3/4)th height of the tower. What is the value of n?

$$\mathrm{Balls}\:\mathrm{are}\:\mathrm{dropped}\:\mathrm{from}\:\mathrm{the}\:\mathrm{roof}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{tower}\:\mathrm{at}\:\mathrm{a}\:\mathrm{fixed}\:\mathrm{interval}\:\mathrm{of}\:\mathrm{time}.\:\mathrm{At}\:\mathrm{the} \\ $$$$\mathrm{moment}\:\mathrm{when}\:\mathrm{9th}\:\mathrm{ball}\:\mathrm{reaches}\:\mathrm{the} \\ $$$$\mathrm{ground}\:\mathrm{the}\:{n}\mathrm{th}\:\mathrm{ball}\:\mathrm{is}\:\left(\mathrm{3}/\mathrm{4}\right)\mathrm{th}\:\mathrm{height} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{tower}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{n}? \\ $$

Question Number 21295    Answers: 1   Comments: 0

For a particle performing uniform circular motion, angular momentum is constant in magnitude but direction keeps changing. Am I right or wrong?

$$\mathrm{For}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{performing}\:\mathrm{uniform} \\ $$$$\mathrm{circular}\:\mathrm{motion},\:\mathrm{angular}\:\mathrm{momentum}\:\mathrm{is} \\ $$$$\mathrm{constant}\:\mathrm{in}\:\mathrm{magnitude}\:\mathrm{but}\:\mathrm{direction} \\ $$$$\mathrm{keeps}\:\mathrm{changing}. \\ $$$$\mathrm{Am}\:\mathrm{I}\:\mathrm{right}\:\mathrm{or}\:\mathrm{wrong}? \\ $$

Question Number 21282    Answers: 0   Comments: 0

soit (u_n )_(n∈N^∗ ) une suite a termes positifs telle que: ∀n∈N^∗ ,Σ_(k=1) ^n u_k ^3 =(Σ_(k=1) ^n u_k )^2 montrer que ∀n∈N^∗ , u_n =n

$${soit}\:\left({u}_{{n}} \right)_{{n}\in\mathbb{N}^{\ast} } {une}\:{suite}\:{a}\:{termes}\:{positifs}\:{telle}\:{que}: \\ $$$$\forall{n}\in\mathbb{N}^{\ast} ,\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{u}_{{k}} ^{\mathrm{3}} =\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{u}_{{k}} \right)^{\mathrm{2}} \\ $$$${montrer}\:{que}\:\forall{n}\in\mathbb{N}^{\ast} ,\:{u}_{{n}} ={n} \\ $$

Question Number 21276    Answers: 1   Comments: 0

Question Number 21249    Answers: 0   Comments: 1

A particle slides down a frictionless parabolic (y = x^2 ) track (A − B − C) starting from rest at point A. Point B is at the vertex of parabola and point C is at a height less than that of point A. After C, the particle moves freely in air as a projectile. If the particle reaches highest point at P, then (a) KE at P = KE at B (b) height at P = height at A (c) total energy at P = total energy at A (d) time of travel from A to B = time of travel from B to P.

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{slides}\:\mathrm{down}\:\mathrm{a}\:\mathrm{frictionless} \\ $$$$\mathrm{parabolic}\:\left({y}\:=\:{x}^{\mathrm{2}} \right)\:\mathrm{track}\:\left({A}\:−\:{B}\:−\:{C}\right) \\ $$$$\mathrm{starting}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{at}\:\mathrm{point}\:{A}.\:\mathrm{Point}\:{B} \\ $$$$\mathrm{is}\:\mathrm{at}\:\mathrm{the}\:\mathrm{vertex}\:\mathrm{of}\:\mathrm{parabola}\:\mathrm{and}\:\mathrm{point}\:{C} \\ $$$$\mathrm{is}\:\mathrm{at}\:\mathrm{a}\:\mathrm{height}\:\mathrm{less}\:\mathrm{than}\:\mathrm{that}\:\mathrm{of}\:\mathrm{point}\:{A}. \\ $$$$\mathrm{After}\:{C},\:\mathrm{the}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{freely}\:\mathrm{in}\:\mathrm{air} \\ $$$$\mathrm{as}\:\mathrm{a}\:\mathrm{projectile}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{reaches} \\ $$$$\mathrm{highest}\:\mathrm{point}\:\mathrm{at}\:{P},\:\mathrm{then} \\ $$$$\left({a}\right)\:\mathrm{KE}\:\mathrm{at}\:{P}\:=\:\mathrm{KE}\:\mathrm{at}\:{B} \\ $$$$\left({b}\right)\:\mathrm{height}\:\mathrm{at}\:{P}\:=\:\mathrm{height}\:\mathrm{at}\:{A} \\ $$$$\left({c}\right)\:\mathrm{total}\:\mathrm{energy}\:\mathrm{at}\:{P}\:=\:\mathrm{total}\:\mathrm{energy}\:\mathrm{at} \\ $$$${A} \\ $$$$\left({d}\right)\:\mathrm{time}\:\mathrm{of}\:\mathrm{travel}\:\mathrm{from}\:{A}\:\mathrm{to}\:{B}\:=\:\mathrm{time}\:\mathrm{of} \\ $$$$\mathrm{travel}\:\mathrm{from}\:{B}\:\mathrm{to}\:{P}. \\ $$

Question Number 21224    Answers: 0   Comments: 1

One mole of a monoatomic real gas satisfies the equation p(V − b) = RT where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by

$$\mathrm{One}\:\mathrm{mole}\:\mathrm{of}\:\mathrm{a}\:\mathrm{monoatomic}\:\mathrm{real}\:\mathrm{gas} \\ $$$$\mathrm{satisfies}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{p}\left(\mathrm{V}\:−\:\mathrm{b}\right)\:=\:\mathrm{RT} \\ $$$$\mathrm{where}\:\mathrm{b}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}.\:\mathrm{The}\:\mathrm{relationship} \\ $$$$\mathrm{of}\:\mathrm{interatomic}\:\mathrm{potential}\:\mathrm{V}\left(\mathrm{r}\right)\:\mathrm{and} \\ $$$$\mathrm{interatomic}\:\mathrm{distance}\:\mathrm{r}\:\mathrm{for}\:\mathrm{the}\:\mathrm{gas}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{by} \\ $$

Question Number 21150    Answers: 0   Comments: 8

Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance ′a′ from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x, is

$$\mathrm{Two}\:\mathrm{particles}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{each}\:\mathrm{are}\:\mathrm{tied} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{ends}\:\mathrm{of}\:\mathrm{a}\:\mathrm{light}\:\mathrm{string}\:\mathrm{of}\:\mathrm{length}\:\mathrm{2}{a}. \\ $$$$\mathrm{The}\:\mathrm{whole}\:\mathrm{system}\:\mathrm{is}\:\mathrm{kept}\:\mathrm{on}\:\mathrm{a}\:\mathrm{frictionless} \\ $$$$\mathrm{horizontal}\:\mathrm{surface}\:\mathrm{with}\:\mathrm{the}\:\mathrm{string}\:\mathrm{held} \\ $$$$\mathrm{tight}\:\mathrm{so}\:\mathrm{that}\:\mathrm{each}\:\mathrm{mass}\:\mathrm{is}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance} \\ $$$$'{a}'\:\mathrm{from}\:\mathrm{the}\:\mathrm{center}\:{P}\:\left(\mathrm{as}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{the}\right. \\ $$$$\left.\mathrm{figure}\right).\:\mathrm{Now},\:\mathrm{the}\:\mathrm{mid}-\mathrm{point}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{string}\:\mathrm{is}\:\mathrm{pulled}\:\mathrm{vertically}\:\mathrm{upwards}\:\mathrm{with} \\ $$$$\mathrm{a}\:\mathrm{small}\:\mathrm{but}\:\mathrm{constant}\:\mathrm{force}\:{F}.\:\mathrm{As}\:\mathrm{a}\:\mathrm{result}, \\ $$$$\mathrm{the}\:\mathrm{particles}\:\mathrm{move}\:\mathrm{towards}\:\mathrm{each}\:\mathrm{other} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{surface}.\:\mathrm{The}\:\mathrm{magnitude}\:\mathrm{of} \\ $$$$\mathrm{acceleration},\:\mathrm{when}\:\mathrm{the}\:\mathrm{separation} \\ $$$$\mathrm{between}\:\mathrm{them}\:\mathrm{becomes}\:\mathrm{2}{x},\:\mathrm{is} \\ $$

Question Number 21148    Answers: 0   Comments: 12

Find the compression in the spring if the system shown below is in equilibrium.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{compression}\:\mathrm{in}\:\mathrm{the}\:\mathrm{spring}\:\mathrm{if} \\ $$$$\mathrm{the}\:\mathrm{system}\:\mathrm{shown}\:\mathrm{below}\:\mathrm{is}\:\mathrm{in} \\ $$$$\mathrm{equilibrium}. \\ $$

Question Number 21145    Answers: 0   Comments: 7

Figure shows an arrangement of blocks, pulley and strings. Strings and pulley are massless and frictionless. The relation between acceleration of the blocks as shown in the figure is

$$\mathrm{Figure}\:\mathrm{shows}\:\mathrm{an}\:\mathrm{arrangement}\:\mathrm{of}\:\mathrm{blocks}, \\ $$$$\mathrm{pulley}\:\mathrm{and}\:\mathrm{strings}.\:\mathrm{Strings}\:\mathrm{and}\:\mathrm{pulley} \\ $$$$\mathrm{are}\:\mathrm{massless}\:\mathrm{and}\:\mathrm{frictionless}.\:\mathrm{The} \\ $$$$\mathrm{relation}\:\mathrm{between}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{blocks}\:\mathrm{as}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{is} \\ $$

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