A mass \(m\) (moving along the \(x-\)axis) with velocity \(v\) collides and sticks to mass of \(3m\) moving vertically upward (along the \(y-\)axis) with velocity \(2v.\) The final velocity of the combination is:
1. \(\frac32v\hat i+\frac14v\hat j\)
2. \(\frac14v\hat i+\frac32 v\hat j\)
3. \(\frac13v\hat i+\frac23 v\hat j\)
4. \(\frac23 v\hat i+\frac13v\hat j\)
 

A ball moving with velocity $2 m{s}^{-1}$ collides head on with another stationery ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in $m{s}^{-1}$) after collision will be 

(1)0,1                                               

(2)1,1

(3)1,0.5                                             

(4)0,2 

An engine pumps water through a hosepipe. Water passes through the pipe and leaves it with a velocity of 2 $m{s}^{-1}.$The mass per unit length of water in the pipe is 100 $kg{m}^{-1}.$What is the power of the engine?

1. 400 W                                       

2. 200 W

3. 100 W                                       

4. 800 W

A particle of mass M starting from rest undergoes uniform acceleration. If the speed acquired in time T is v, the power delivered to the particle is 

(1) $\frac{{\mathrm{Mv}}^2}{\mathrm{T}}$                                 

(2) $\frac{1}{2}\frac{{\mathrm{Mv}}^2}{{\mathrm{T}}^2}$

(3) $\frac{{\mathrm{Mv}}^2}{{\mathrm{T}}^2}$                                   

(4) $\frac{1}{2}\frac{{\mathrm{Mv}}^2}{\mathrm{T}}$

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of $12 {\mathrm{ms}}^{-1}$ and 2 kg second part moving with a velocity of $8 {\mathrm{ms}}^{-1}.$ If the third part flies off with a velocity of $4 {\mathrm{ms}}^{-1},$ its mass would be 

(a) $5 \mathrm{kg}$                                           (b) $7 \mathrm{kg}$

(c) $17 \mathrm{kg}$                                          (d) $3 \mathrm{kg}$

A body of mass 1 kg is thrown upwards with a velocity $20 {\mathrm{ms}}^{-1}.$ It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? $\left(\mathrm{g}=10 {\mathrm{ms}}^{-2}\right)$

(a) 20 J                               (b) 30 J

(c) 40 J                                (d) 10 J

A block of mass \(M\) is attached to the lower end of a vertical spring. The spring is hung from the ceiling and has a force constant value of \(k.\) The mass is released from rest with the spring initially unstretched. The maximum extension produced along the length of the spring will be:
1. \(Mg/k\)
2. \(2Mg/k\)
3. \(4Mg/k\)
4. \(Mg/2k\)

A shell of mass 200g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is -

(1) 100 $m{s}^{-1}$

(2) 80 $m{s}^{-1}$

(3) 40 $m{s}^{-1}$

(4) 120 $m{s}^{-1}$

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

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