$A$ 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:

$A$ truck of mass $M$ and a car of mass $\frac{M}{10}$ moving with the same momentum are brought to a halt by the application of the same braking force. The ratio of the distances travelled by the truck and the car before they come to a stop is

As shown in the figure,a block of mass $2 \ kg$ is released from point $P$. It slides $0.5 \ m$ on the inclined plane before hitting a spring. The spring constant is $4000 \ N/m$. The coefficient of friction between the block and the inclined plane is $0.3$. The compression in the spring will be ............... $mm$.

$A$ block of mass $m$ starts from rest and slides down a frictionless semi-circular track from a height $h$ as shown. When it reaches the lowest point of the track,it collides with a stationary piece of putty also having mass $m$. If the block and the putty stick together and continue to slide,the maximum height that the block-putty system could reach is:

$A$ section of a fixed smooth circular track of radius $R$ in a vertical plane is shown in the figure. $A$ block is released from position $A$ and leaves the track at $B$. The radius of curvature of its trajectory when it just leaves the track at $B$ is:

$A$ ball is dropped from a height of $5\,m$ onto a sandy floor and penetrates the sand up to $1\,m$ before coming to rest. The retardation of the ball in sand (assuming it to be uniform) will be ................ $m/s^2$.