Two identical balls \(\mathrm{A}\) and \(\mathrm{B}\) having velocities of \(0.5~\text{m/s}\) and \(-0.3~\text{m/s}\) respectively collide elastically in one dimension. The velocities of \(\mathrm{B}\) and \(\mathrm{A}\) after the collision respectively will be:
1. \(-0.5 ~\text{m/s}~\text{and}~0.3~\text{m/s}\) 
2. \(0.5 ~\text{m/s}~\text{and}~-0.3~\text{m/s}\)
3. \(-0.3 ~\text{m/s}~\text{and}~0.5~\text{m/s}\)
4. \(0.3 ~\text{m/s}~\text{and}~0.5~\text{m/s}\)

Subtopic:  Collisions |
 58%
From NCERT
NEET - 2016
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A body of mass 1 kg begins to move under the action of a time dependent force \(F = 2 t\) \(\hat{i} + 3 t^{2}\ \hat{j}\) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along X and Y axis, What power will be developed by the force at the time (t) ?

1. \(\left(2 t^{2} + 4 t^{4}\right) W\)         

2. \(\left(2 t^{3} + 3 t^{4}\right) W\)

3. \(\left(2 t^{3} + 3 t^{5}\right) W\)         

4. \(\left(2 t + 3 t^{3}\right) W\)

Subtopic:  Power |
 69%
From NCERT
NEET - 2016
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What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

1. 2gR

2. 3gR

3. 5gR

4. gR
 

Subtopic:  Work Energy Theorem |
 78%
From NCERT
NEET - 2016
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A block of mass \(10\) kg, moving in the \(x\text-\)direction with a constant speed of \(10\) ms-1, is subjected to a retarding force \(F=0.1x\) J/m during its travel from \(x =20\) m to \(30\) m. Its final kinetic energy will be:

1. \(475\) J 2. \(450\) J
3. \(275\) J 4. \(250\) J
Subtopic:  Work Done by Variable Force |
 73%
From NCERT
NEET - 2015
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A particle of mass m is driven by a machine that delivers a constant power of k watts. If the particle starts from rest the force on the particle at time t is:

(1) mk2t-1/2

(2) mkt-1/2

(3) 2mkt-1/2

(4) 12mkt-1/2

Subtopic:  Power |
From NCERT
NEET - 2015
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Two particles of masses m1,m2 move with initial velocities u1 and u2. On collision, one of the particles get excited to higher level, after absorbing energy ε. If final velocities of particles be v1 and v2, then we must have

(a)m12u1+m22u2-ε=m12v1+m22v2

(b)12m1u12+12m2u2=12m1v12+12m2v22-ε

(c)12m1u12+12m2u22-ε=12m1v12+12m2v22

(d)12m12u12+12m22u22+ε=12m12v12+12m22v22

Subtopic:  Work Energy Theorem |
 58%
From NCERT
NEET - 2015
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A ball is thrown vertically downwards from a height of \(20\) m with an initial velocity \(v_0\). It collides with the ground, loses \(50\%\) of its energy in a collision and rebounds to the same height. The initial velocity \(v_0\) is: (Take \(g = 10~\text{m/s}^2\))
1. \(14~\text{m/s}\)
2. \(20~\text{m/s}\)
3. \(28~\text{m/s}\)
4. \(10~\text{m/s}\)

Subtopic:  Conservation of Mechanical Energy |
 66%
From NCERT
NEET - 2015
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Two particles A and B. move with constant velocities v1 and v2. At the initial moment, their position vectors are r1 and r2 respectively. The condition for particles A and B for their collision is-


(1) r1-r2r1-r2=v2-v1v2-v1

(2) r1·v1=r2·v2

(3) r1×v1=r2×v2

(4) r1-r2=v1-v2

Subtopic:  Collisions |
 72%
NEET - 2015
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On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle θ to its initial direction and has a speed v/3. The second block's speed after the collision is:

(1)2√2v/3
 

(2)3v/4
 

(3)3v/√2
 

(4)√3v/2

Subtopic:  Collisions |
 63%
From NCERT
NEET - 2015
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The force F acting on a particle of mass m is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is:
     
1. 24 Ns

2. 20 Ns

3. 12 Ns

4. 6 Ns

Subtopic:  Collisions |
 80%
From NCERT
NEET - 2014
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