$A$ ball is released from the top of a tower. The ratio of work done by the force of gravity in the first,second,and third second of the motion of the ball is:

If a skater of mass $3 \,kg$ has an initial speed of $32 \,m/s$ and a second skater of mass $4 \,kg$ has a speed of $5 \,m/s$. After a perfectly inelastic collision,they move together with a speed of $5 \,m/s$. Calculate the loss in kinetic energy.

$A$ $0.5 \, kg$ block moving at a speed of $12 \, ms^{-1}$ compresses a spring through a distance of $30 \, cm$ when its speed is halved. The spring constant of the spring in $N m^{-1}$ is:

$A$ ball of mass $0.2 \ kg$ is at rest at a height of $5 \ m$. $A$ bullet of mass $0.01 \ kg$ moving horizontally with a velocity $V \ m/s$ strikes the center of the ball. After the collision,the ball and the bullet move independently. The ball hits the ground at a distance of $20 \ m$ and the bullet hits the ground at a distance of $100 \ m$ from the base of the pillar. What is the initial velocity $V$ of the bullet in $m/s$?

$A$ small block of mass $200 \ g$ is placed on a horizontal slab at a height of $2 \ m$ above the floor. The block is pressed against a horizontal spring fixed at one end to compress the spring by $10.0 \ cm$. Upon releasing,the block moves horizontally until it leaves the spring. Calculate the horizontal distance covered by the block after leaving the slab and just before hitting the ground. The spring constant is $50 \ N \ m^{-1}$. (Assume $g = 10 \ m \ s^{-2}$) (in $m$)

$A$ man is slipping on a frictionless inclined plane and a bag falls down from the same height. Then the velocity of both is related as