JEE Main20205 Sep 2020Evening ShiftPhysicsLaws of MotionActual
A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate d M ( t ) d t = 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- b v 3 M ( t )
- C- 2 b v 3 M ( t )
- D- b v 3 2 M ( t )
Correct answer
B. - b v 3 M ( t )
Step-by-step solution
dM ( t ) dt = - bv 2 in free space no external force so there in only thrust force on rocket f i n   = d M d t V r e l M a = - b v 2 ( t ) v a = - bv 3 M ( t )