A particle of mass m is moving in a straight line with momentum p. Starting at time $t = 0$, a force $F = k \mathrm { t }$ acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here $k$ is a constant. The value of T is
(1) $2\sqrt { \frac { k } { p } }$
(2) $2\sqrt { \frac { \mathrm { p } } { k } }$
(3) $\sqrt { \frac { 2k } { p } }$
(4) $\sqrt { \frac { 2p } { \mathrm { k } } }$

A circular disc of mass M and radius R is rotating about its axis with angular speed $\omega _ { 1 }$. If another stationary disc having radius $\frac { \mathrm { R } } { 2 }$ and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed $\omega _ { 2 }$. The energy lost in the process is $p \%$ of the initial energy. Value of $p$ is $\_\_\_\_$

A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of mass 0.1 kg moving in a straight line with velocity $80\,\mathrm{m\,s^{-1}}$ hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in $\mathrm{rad\,s^{-1}}$) of the rod immediately after the collision will be $\_\_\_\_$

Two billiard balls of equal mass 30 g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed, then the ratio of the magnitude of impulses imparted to ball $a$ and ball $b$ by the wall along $X$ direction is:
(1) $1 : 1$
(2) $\sqrt{2} : 1$
(3) $2 : 1$
(4) $1 : \sqrt{2}$

A ball of mass 0.15 kg hits the wall with its initial speed of $12 \mathrm{~m~s}^{-1}$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N, calculate the time duration of the contact of ball with the wall.
(1) 0.018 s
(2) 0.036 s
(3) 0.009 s
(4) 0.072 s

A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The impulse imparted to the ball is $\_\_\_\_$ Ns.

An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of $250 \mathrm{~m}\mathrm{~s}^{-1}$ to keep it in position. The number of bullets fired per second by the machine gun is:
(1) 50
(2) 25
(3) 100
(4) 5

A bullet of 10 g leaves the barrel of gun with a velocity of $600 \mathrm{~m~s}^{-1}$. If the barrel of gun is 50 cm long and mass of gun is 3 kg, then value of impulse supplied to the gun will be:
(1) 6 N s
(2) 3 N s
(3) 36 N s
(4) 12 N s

A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m . The impulse of force imparted by the ground to the body is given by: (given $g = 9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ )
(1) $4.32 \mathrm {~kg} \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $43.2 \mathrm {~kg} \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $23.9 \mathrm {~kg} \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $2.39 \mathrm {~kg} \mathrm {~m} \mathrm {~s} ^ { - 1 }$