A car accelerates from rest to $u\,m / s$. The energy spent in this process is $E\,J$. The energy required to accelerate the car from $u\,m / s$ to $2u\,m / s$ is $nE\,J$. The value of $n$ is ..............

Two solids $A$ and $B$ of mass $1\, kg$ and $2\, kg$ respectively are moving with equal linear momentum. The ratio of their kinetic energies $(K.E.)_{ A }:( K.E. )_{ B }$ will be $\frac{ A }{1},$ so the value of $A$ will be ..... .

A projectile is fired with $KE$ of $1\,kJ$. If the range is maximum, .......... $J$ is its $KE$ at the highest point.

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 $...........kJ.$

Two masses of $1 \,gm$ and $4 \,gm$ are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

Two bodies of masses $m$ and $4 \,m$ are moving with equal $K.E.$ The ratio of their linear momentums is