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JEE Main 20205 SeptemberEvening Shift

Exam: JEE Main
Year: 2020
Date: 5 September
Shift: Evening Shift
Subject: Physics
Chapter: Laws of Motion

JEE Main 2020 · 5 September · Evening Shift · Physics · Laws of Motion

A spaceship in space sweeps stationary interplanetary dust. As a...

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate

\dfrac{dM ( t )}{dt} = b{v}^{2} ( t ) ,

where

v ( t )

is its instantaneous velocity. The instantaneous acceleration of the satellite is:

Options

A $- b{v}^{3} ( t )$
B $\dfrac{- b{v}^{3}}{M ( t )}$
C $- \dfrac{2b{v}^{3}}{M ( t )}$
D $- \dfrac{b{v}^{3}}{2M ( t )}$

Correct answer

B. $\dfrac{- b{v}^{3}}{M ( t )}$

Step-by-step solution

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

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

{f}_{in} = \dfrac{dM}{dt}\left({V}_{rel}\right)

Ma = \left(\dfrac{- b{v}^{2}}{( t )}\right)v

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

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