A ball of mass $2\,kg$ and another of mass $4\,kg$ are dropped together from a $60$ feet tall building. After a fall of $30$ feet each towards earth, their respective kinetic energies will be in the ratio of

A lift of mass $M =500\,kg$ is descending with speed of $2\,ms ^{-1}$. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of $2\,ms ^{-2}$. The kinetic energy of the lift at the end of fall through to a distance of $6 m$ will be $...........kJ.$

The slope of kinetic energy displacement curve of a particle in motion is

Two identical uniform discs roll without slipping on two different surfaces $AB$ and $CD$ (see figure) starting at $A$ and $C$ with linear speeds $v _1$ and $v _2$, respectively, and always remain in contact with the surfaces. If they reach $B$ and $D$ with the same linear speed and $v_1=3 \ m / s$, then $v_2$ in $m / s$ is $\left(g=10 \ m / s ^2\right)$

If the kinetic energy of a body becomes four times of its initial value, then new momentum will

A bullet moving with a speed of $100$ $m{s^{ - 1}}$can just penetrate two planks of equal thickness. Then the number of such planks penetrated by the same bullet when the speed is doubled will be