$A$ 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 ................ $m/s^2$.

$A$ bullet moving with a velocity of $100\, m/s$ can just penetrate two planks of equal thickness. The number of such planks penetrated by the same bullet,when the velocity is doubled,will be

Consider a frictionless ramp on which a smooth object is made to slide down from an initial height $h$. The distance $d$ necessary to stop the object on a flat track (of coefficient of friction $\mu$), kept at the ramp end, is:

Two cars,both of mass $m$,collide and stick together. Prior to the collision,one car had been traveling north at speed $2v$,while the second was traveling at speed $v$ at an angle $\phi$ south of east (as indicated in the figure). The magnitude of the velocity of the two-car system immediately after the collision is:

Two bodies have kinetic energies in the ratio $16: 9$. If they have the same linear momentum,the ratio of their masses respectively is

Blocks of masses $m, m, 2m, 4m$ and $8m$ are arranged in a line on a frictionless floor. Another block of mass $m$,moving with speed $v$ along the same line (see figure) collides with the first mass $m$ in a perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass $8m$ starts moving,the total energy loss is $p\%$ of the original energy. The value of $p$ is close to: