Two trolleys of mass $m$ and $3m$ are connected by a spring. They are compressed and released; once released,they move off in opposite directions and come to rest after covering distances $S_1$ and $S_2$ respectively. Assuming the coefficient of friction to be uniform,the ratio of distances $S_1:S_2$ is:

$A$ block of mass $M = 1 \ kg$ is released from rest at the top of a smooth track of radius $R = 40 \ m$. The block slides along the track without toppling,and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point $Q$ (where the radius makes an angle of $30^{\circ}$ with the horizontal),as shown in the figure,is $150 \ J$. (Take the acceleration due to gravity,$g = 10 \ m s^{-2}$)
$1.$ The speed of the block when it reaches the point $Q$ is:
$(A) 5 \ m s^{-1}$ $(B) 10 \ m s^{-1}$ $(C) 10\sqrt{3} \ m s^{-1}$ $(D) 20 \ m s^{-1}$
$2.$ The magnitude of the normal reaction that acts on the block at the point $Q$ is:
$(A) 7.5 \ N$ $(B) 8.6 \ N$ $(C) 11.5 \ N$ $(D) 22.5 \ N$
Give the answers for question $1$ and $2$.

$A$ ball of mass $m$ moves with speed $v$ and strikes a wall having infinite mass and it returns with the same speed. Then the work done by the ball on the wall is:

$A$ body of mass $4 \ kg$ is moving with a momentum of $8 \ kg \ m/s$. $A$ force of $0.2 \ N$ acts on it in the direction of motion for $10 \ s$. The increase in kinetic energy in joules is:

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
$(a)$ Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.
$(b)$ Work done by gravitational force in the above case.
$(c)$ Work done by friction on a body sliding down an inclined plane.
$(d)$ Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity.
$(e)$ Work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

$A$ body of mass $0.5 \ kg$ is supplied with a power $P$ (in watt) which varies with time $t$ (in second) as $P = 3t^2 + 3$. If the velocity of the body at time $t = 0$ is zero,then the velocity of the body at time $t = 3 \ s$ is (in $ms^{-1}$)