Verified Solution • 2025–26 Session moderate

QJEEM20Ph9d03: JEE Main 2020 Physics - Class 11 JEEM20Ph9d03 Solution: A spaceship in space sweeps stationary interplanetary dust. As…

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

Multiple Choice Options

  • A - {{b{v^3}}\left( t \right)}}
  • B −2bv3M(t)- {{2b{v^3}} \over {M\left( t \right)}}
  • C −bv3M(t)- {{b{v^3}} \over {M\left( t \right)}}
  • D −bv32M(t)- {{b{v^3}} \over {2M\left( t \right)}}

Step-by-Step Verified Solution

Given dM(t)dt{{dM\left( t \right)} \over {dt}} = bv2(t)

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

Fthrust = v dmdt{{dm} \over {dt}}

Force on satellite = −v→dm(t)dt- \overrightarrow v {{dm\left( t \right)} \over {dt}}

M(t)a = – v (bv2)

⇒\Rightarrow a = −bv3M(t)- {{b{v^3}} \over {M\left( t \right)}}

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