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Question Number 23548 Answers: 0 Comments: 3

Question Number 23585 Answers: 0 Comments: 0

No work is done by a force on an object if (1) the object is stationary but the point of application of the force moves on the object (2) the object moves in such a way that the point of application of the force remains fixed (3) the force is always perpendicular to its velocity (4) the force is always perpendicular to its acceleration.

$$\mathrm{No}\:\mathrm{work}\:\mathrm{is}\:\mathrm{done}\:\mathrm{by}\:\mathrm{a}\:\mathrm{force}\:\mathrm{on}\:\mathrm{an}\:\mathrm{object}\:\mathrm{if} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{the}\:\mathrm{object}\:\mathrm{is}\:\mathrm{stationary}\:\mathrm{but}\:\mathrm{the} \\ $$$$\mathrm{point}\:\mathrm{of}\:\mathrm{application}\:\mathrm{of}\:\mathrm{the}\:\mathrm{force}\:\mathrm{moves} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{object} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{the}\:\mathrm{object}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{way} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\:\mathrm{application}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{force}\:\mathrm{remains}\:\mathrm{fixed} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{the}\:\mathrm{force}\:\mathrm{is}\:\mathrm{always}\:\mathrm{perpendicular}\:\mathrm{to} \\ $$$$\mathrm{its}\:\mathrm{velocity} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{the}\:\mathrm{force}\:\mathrm{is}\:\mathrm{always}\:\mathrm{perpendicular}\:\mathrm{to} \\ $$$$\mathrm{its}\:\mathrm{acceleration}. \\ $$

Question Number 23584 Answers: 1 Comments: 0

Question Number 23539 Answers: 1 Comments: 0

∫tan^6 x dx

$$\int\mathrm{tan}\:^{\mathrm{6}} \mathrm{x}\:\mathrm{dx} \\ $$

Question Number 23537 Answers: 1 Comments: 8

Question Number 23531 Answers: 1 Comments: 3

Question Number 23524 Answers: 0 Comments: 0

Question Number 23523 Answers: 0 Comments: 0

The order and degree of the differential equation are y^(11) =(y−y^1^3 )^(2/3)

$${The}\:{order}\:{and}\:{degree}\:{of}\:{the}\:{differential}\:{equation}\:{are}\:{y}^{\mathrm{11}} =\left({y}−{y}^{\mathrm{1}^{\mathrm{3}} } \right)^{\mathrm{2}/\mathrm{3}} \\ $$

Question Number 23522 Answers: 0 Comments: 1

the particular integral of the differential equation f(D)y=e^(ax) where f(D)=(D−a)g(D),g(a)≠0 is

$${the}\:{particular}\:{integral}\:{of}\:{the}\:{differential}\:{equation}\:{f}\left({D}\right){y}={e}^{{ax}} {where}\:{f}\left({D}\right)=\left({D}−{a}\right){g}\left({D}\right),{g}\left({a}\right)\neq\mathrm{0}\:{is} \\ $$

Question Number 23520 Answers: 0 Comments: 3

A wooden block of mass 10 gm is dropped from the top of a tower 100 m high. Simultaneously, a bullet of mass 10 gm is fired from the foot of the tower vertically upwards with a velocity of 100 m/sec. If the bullet is embedded in it, how high will it rise above the tower before it starts falling? (Consider g = 10 m/sec^2 )

$$\mathrm{A}\:\mathrm{wooden}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{10}\:\mathrm{gm}\:\mathrm{is} \\ $$$$\mathrm{dropped}\:\mathrm{from}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tower}\:\mathrm{100}\:\mathrm{m} \\ $$$$\mathrm{high}.\:\mathrm{Simultaneously},\:\mathrm{a}\:\mathrm{bullet}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\mathrm{10}\:\mathrm{gm}\:\mathrm{is}\:\mathrm{fired}\:\mathrm{from}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tower} \\ $$$$\mathrm{vertically}\:\mathrm{upwards}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of} \\ $$$$\mathrm{100}\:\mathrm{m}/\mathrm{sec}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{bullet}\:\mathrm{is}\:\mathrm{embedded}\:\mathrm{in} \\ $$$$\mathrm{it},\:\mathrm{how}\:\mathrm{high}\:\mathrm{will}\:\mathrm{it}\:\mathrm{rise}\:\mathrm{above}\:\mathrm{the}\:\mathrm{tower} \\ $$$$\mathrm{before}\:\mathrm{it}\:\mathrm{starts}\:\mathrm{falling}?\:\left(\mathrm{Consider}\:{g}\:=\right. \\ $$$$\left.\mathrm{10}\:\mathrm{m}/\mathrm{sec}^{\mathrm{2}} \right) \\ $$

Question Number 23535 Answers: 0 Comments: 0

if a compound statement is made up of three simple statements then the number of rows in the truth table is

$${if}\:{a}\:{compound}\:{statement}\:{is}\:{made}\:{up}\:{of}\:{three}\:{simple}\:{statements}\:{then}\:{the}\:{number}\:{of}\:{rows}\:{in}\:{the}\:{truth}\:{table}\:{is} \\ $$

Question Number 23508 Answers: 1 Comments: 1

Question Number 23518 Answers: 0 Comments: 5

A ball of mass 1 kg moving with velocity 3 m/s collides with spring of natural length 2 m and force constant 144 N/m. What will be length of compressed spring?

$$\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{velocity} \\ $$$$\mathrm{3}\:\mathrm{m}/\mathrm{s}\:\mathrm{collides}\:\mathrm{with}\:\mathrm{spring}\:\mathrm{of}\:\mathrm{natural} \\ $$$$\mathrm{length}\:\mathrm{2}\:\mathrm{m}\:\mathrm{and}\:\mathrm{force}\:\mathrm{constant}\:\mathrm{144}\:\mathrm{N}/\mathrm{m}. \\ $$$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{length}\:\mathrm{of}\:\mathrm{compressed} \\ $$$$\mathrm{spring}? \\ $$

Question Number 23492 Answers: 0 Comments: 5

Question Number 23489 Answers: 1 Comments: 2

A rectangular wire frame ABCD is in vertical plane is moving with a constant acceleration a into the plane. Direction of gravity is shown in figure. A collar can move on wire AC of length l. Coefficient of friction between wire and collar is μ. Find (i) The minimum acceleration a so that collar does not slip on wire. (ii) The time taken by collar to reach C if acceleration is half the value calculated in part (i)

$$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{wire}\:\mathrm{frame}\:{ABCD}\:\mathrm{is}\:\mathrm{in} \\ $$$$\mathrm{vertical}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{a}\:\mathrm{constant} \\ $$$$\mathrm{acceleration}\:{a}\:\mathrm{into}\:\mathrm{the}\:\mathrm{plane}.\:\mathrm{Direction} \\ $$$$\mathrm{of}\:\mathrm{gravity}\:\mathrm{is}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{figure}.\:\mathrm{A}\:\mathrm{collar} \\ $$$$\mathrm{can}\:\mathrm{move}\:\mathrm{on}\:\mathrm{wire}\:{AC}\:\mathrm{of}\:\mathrm{length}\:{l}. \\ $$$$\mathrm{Coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{between}\:\mathrm{wire} \\ $$$$\mathrm{and}\:\mathrm{collar}\:\mathrm{is}\:\mu.\:\mathrm{Find} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{The}\:\mathrm{minimum}\:\mathrm{acceleration}\:{a}\:\mathrm{so}\:\mathrm{that} \\ $$$$\mathrm{collar}\:\mathrm{does}\:\mathrm{not}\:\mathrm{slip}\:\mathrm{on}\:\mathrm{wire}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{The}\:\mathrm{time}\:\mathrm{taken}\:\mathrm{by}\:\mathrm{collar}\:\mathrm{to}\:\mathrm{reach}\:{C} \\ $$$$\mathrm{if}\:\mathrm{acceleration}\:\mathrm{is}\:\mathrm{half}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{calculated}\:\mathrm{in}\:\mathrm{part}\:\left(\mathrm{i}\right) \\ $$

Question Number 23488 Answers: 0 Comments: 0

area of a(1−cos θ)

$${area}\:{of}\:{a}\left(\mathrm{1}−\mathrm{cos}\:\theta\right) \\ $$

Question Number 23485 Answers: 0 Comments: 0

(1/(cos (x−a)cos (x−b)))

$$\frac{\mathrm{1}}{\mathrm{cos}\:\left({x}−{a}\right)\mathrm{cos}\:\left({x}−{b}\right)} \\ $$

Question Number 23481 Answers: 0 Comments: 5

Which of the diagrams represents variation of total mechanical energy of a pendulum oscillating in air as function of time?

$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{diagrams}\:\mathrm{represents} \\ $$$$\mathrm{variation}\:\mathrm{of}\:\mathrm{total}\:\mathrm{mechanical}\:\mathrm{energy}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{pendulum}\:\mathrm{oscillating}\:\mathrm{in}\:\mathrm{air}\:\mathrm{as}\:\mathrm{function} \\ $$$$\mathrm{of}\:\mathrm{time}? \\ $$

Question Number 23479 Answers: 0 Comments: 0

Common solution. (d/dy)(u_x +u)+2x^2 y(u_x +u)=0.