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

A body of mass m is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The change in potential energy of the body will be
\(1.~2mgR\)
\(2.~\frac{2}{3}mgR\)
\(3.~3mgR\)
\(4.~\frac{1}{3}mgR\)




 

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

magnitude \(P_0\). The instantaneous velocity of this car is proportional to:
1. \(t^2 P_0\)
2. \(t^{\frac{1}{2}}\)
3. \(t^{\frac{-1}{2}}\)
4. \(\frac{t}{\sqrt{m}}\)

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