A bomb of mass $9\,kg$ explodes into $2$ pieces of mass $3\,kg$ and $6\,kg.$ The velocity of mass $3\,kg$ is $1.6\, m/s$, the K.E. of mass $6\,kg$ is ............ $J$

If the kinetic energy of a body is directly proportional to time $t,$ the magnitude of force acting on the body is

$(i)$ directly proportional to $\sqrt t$
$(ii)$  inversely proportional to  $\sqrt t$
$(iii)$ directly proportional to the speed of the body
$(iv)$ inversely proportional to the speed of body

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

The same retarding force is applied to stop a train. The train stops after $80 m$. If the speed is doubled, then the distance will be

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

Tripling the speed of the motor car multiplies the distance needed for stopping it by