$A$ truck and a car are moving with equal velocity. On applying the brakes,both will stop after a certain distance. Which of the following is true?

By how much should the spring be compressed by the block so that the centripetal force at point $P$ is $mg$?

$A$ ball falls freely from rest on to a hard horizontal floor and repeatedly bounces. If the velocity of the ball just before the first bounce is $7 \text{ m/s}$ and the coefficient of restitution is $0.75$. The total distance travelled by the ball before it comes to rest is (acceleration due to gravity $= 10 \text{ m/s}^2$) (in $\text{ m}$)

$A$ target is made of two plates,one of wood and the other of iron. The thickness of the wooden plate is $4\,cm$ and that of the iron plate is $2\,cm$. $A$ bullet fired goes through the wood first and then penetrates $1\,cm$ into the iron. $A$ similar bullet fired with the same velocity from the opposite direction goes through the iron first and then penetrates $2\,cm$ into the wood. If $a_1$ and $a_2$ are the retardations offered to the bullet by the wood and iron plates respectively,then:

$A$ bullet of mass $4\,g$ is fired horizontally with a speed of $300\,m/s$ into a $0.8\,kg$ block of wood at rest on a table. If the coefficient of friction between the block and the table is $0.3$,how far will the block slide approximately (in $,m$)?

$A$ sphere of mass $m$,moving with velocity $V$,enters a hanging bag of sand and stops. If the mass of the bag is $M$ and it is raised by height $h$,then the velocity of the sphere was