Physics MCQs for NEET — Practice Questions with Answers

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A particle moves in the x-y plane with velocity vx=8t-2 and vy=2. If it passes through the point x=14 and y=4 at t=2 sec. The equation of the path is

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Explanation

 

 

vx=8t-2                                     vy=2dxdt=8t-2                                  dydt=2dx=8t-2dt                      dy=2dtx=4t2-2t+c                              y=2t+c1At  t=2s, x=14                          At t=2s, y=414=422-22+c                     4=22+c1      c=2                                               c1=0x=4t2-2t+2                              y=2t Putting t=y2 in xx=4y22-2y2+2x=y2-y+2

A motor boat of mass m moving along a lake with velocity V0. At t=0, the engine of the boat is shut down. Magnitude of resistance force offered to the boat is equal to rV. (V is instantaneous speed). What is the total distance covered till it stops completely? Hint: Fx=mVdVdx=-rV

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Explanation

 

mVdVdx=-rVdVdx = -rmvo0dv =-rm 0sdxs =mvor

A particle is moving along positive x-axis. Its position varies as x=t3-3t2+12t+20, where x is in meters and t is in seconds.

Initial velocity of the particle is

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Explanation

v=dxdt     =3t2 -6t +12At t=0v=12 m/s

A particle is moving along positive x-axis. Its position varies as x=t3-3t2+12t+20, where x is in meters and t is in seconds.

Initial acceleration of the particle is

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Explanation

x=t3-3t2+12t+20v=dxdt=3t2-6t+12a=dvdt=6t-6at t=0, a=-6 m/s2

A particle is moving along positive x-axis. Its position varies as x=t3-3t2+12t+20, where x is in meters and t is in seconds.

Velocity of the particle when its acceleration zero is

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Explanation

v=dxdt=3t2-6t+12a=dvdt=6t-6When a=0, 6t-6=0t=1 secv at 1 sec.=9m/s

Two forces F1=2i^+2j^ N and F2=3j^+4k^ N are acting on a particle.

The resultant force acting on particle is:

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Explanation

Resultant force = F1+F2=2i^+5j^+4k^

Two forces F1=2i^+2j^ N and F2=3j^+4k^ N are acting on a particle.

The angle between F1 & F2 is:

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Explanation

angle between F1 & F2 is given by-

cos θ=F1.F2F1.F2=622×5=352θ=cos-1352

Two forces F1=2i^+2j^ N and F2=3j^+4k^ N are acting on a particle.

The magnitude of the component of force F1 along force F2 is:

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Explanation

Magnitude of the forcee F1 along F2=F1cosθ where θ is the angle between two forces

F1cosθ=F1×F1.F2F1F2=F1.F2F2=65N

A=4i+4j-4k and B=3i+j+4k, then angle between vectors A and B is:

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Explanation

The angle between two vector will be given by-

cosθ=A.BAB=(4i^+4j^-4k^).(3i^+j^+4k^)(4)2+(4)2+(-4)2×(3)2+(1)2+(4)2=043×26=0cosθ=cos90°θ=90°

The acceleration of a particle starting from rest varies with time according to relation, a=α t+β. Find the velocity of the particle at time instant t.

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Explanation

Given that, a=dvdt=αt+β

0vdv=0t(αt+β)dt=αt22+βt0t      v=αt22+βt

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