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

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate dM(t)dt=bv2(t), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is:
  1. -bv3(t)
  2. -bv3M(t)
  3. -2bv3M(t)
  4. -bv32M(t)

Solution

dM(t)dt=-bv2
in free space no external force so there in only thrust force on rocket
fin =dMdtVrel
Ma=-bv2(t)v
a=-bv3M(t)

Asked in: JEE Main 2020 (05 Sep Shift 2)

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