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. \(10~\text{m/s}\)

Two particles A and B. move with constant velocities v₁ and v₂. At the initial moment, their position vectors are $r_1$ and $r_2$ respectively. The condition for particles A and B for their collision is-


(1) $\frac{r_1-r_2}{\left|r_1-r_2\right|}=\frac{v_2-v_1}{\left|v_2-v_1\right|}$

(2) $r_1·v_1=r_2·v_2$

(3) _{$r_1\times v_1=r_2\times v_2$}

(4) r₁-r₂=v₁-v₂

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

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

A uniform force of (3i + j) N acts on a particle of mass 2 kg. Hence the particle is displaced from position (2i+k) m to position (4i+3j-k) m. The work done by the force on the particle is-

(1) 9J

(2) 6J

(3) 13J

(4) 15J

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms^-1 and the second part of mass 2kg moves with 8 ms^-1 speed. If the third part flies off with 4 ms^-1 speed, then its mass is

(1) 3kg
 

(2) 5kg
 

(3) 7kg
 

(4) 17kg

Two spheres A and B of masses $m_1 and m_2$ respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction.The mass A moves after collision in the direction

(1)same as that of B

(2)opposite to that of B

(3)$\theta ={\tan }^{-1}\left(\frac{1}{2}\right)to the x‐axis$

(4)$\theta ={\tan }^{-1}\left(\frac{-1}{2}\right)to the x‐axis$

The potential energy of a system increases if work is done

(1) by the system against a conservative force 

(2) by the system against a nonconservative force

(3) upon the system by a conservative force

(4) upon the system by a nonconservative force

Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done on the particle during its displacement of 12 m is

(a) 21 J                                                  (b) 26 J

(c) 13 J                                                   (d) 18 J