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
$(i), (ii)$
$(i), (iii)$
$(ii), (iv)$
$(i), (iv)$
A body moving with speed $v$ in space explodes into two piece of masses in the ratio $1 : 3.$ If the smaller piece comes to rest, the speed of the other piece is
Force acting on a particle moving in a straight line varies with the velocity of the particle as $F = \frac{K}{\upsilon }$ where $K$ is a constant. The work done by this force in time $t$ is
Three particles of masses $10g, 20g$ and $40g$ are moving with velocities $10\widehat i,10\widehat j$ and $10\widehat k$ $m/s$ respectively. If due to some mutual interaction, the first particle comes to rest and the velocity of second particle becomes $\left( {3\widehat i + 4\widehat j\,\,} \right)\, m/s$, then the velocity of third particle is
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