Laws of Motion

JEE Main level, single correct, medium

40 of 210

Question 40 of 210

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate dM(t)dt=bv2(t),\dfrac{dM(t)}{dt}=b{v}^{2}(t), where v(t)v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is:

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Answer: (B) −bv3M(t)\dfrac{-b{v}^{3}}{M(t)}

dM(t)dt=−bv2\dfrac{dM(t)}{dt}=-{bv}^{2}
in free space no external force so there in only thrust force on rocket
fin=dMdt(Vrel){f}_{in}=\dfrac{dM}{dt}\left({V}_{rel}\right)
Ma=(−bv2(t))vMa=\left(\dfrac{-b{v}^{2}}{(t)}\right)v
a=−bv3M(t)a=\dfrac{-{bv}^{3}}{M(t)}

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