A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate (dM(t))/dt=bv^2(t), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is:

Q51 / 75 · JEE Main 2020 (05 Sep Shift 2) · Physics

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\frac{d M (t)}{d t} = b v^{2} (t),$ where $v (t)$ is its instantaneous velocity. The instantaneous acceleration of the satellite is:

\frac{dM (t)}{dt} = - {bv}^{2}

in free space no external force so there in only thrust force on rocket

f_{i n} = \frac{d M}{d t} (V_{r e l})

M a = (\frac{- b v^{2}}{(t)}) v

a = \frac{- {bv}^{3}}{M (t)}

Hence, the correct answer is option: 'B'.