JEE PYQ: Laws Of Motion Question 16
Question 16 - 2020 | 05 Sep Shift 2] (MCQ)
A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\frac{dM(t)}{dt} = bv^2(t)$, where $v(t)$ is its instantaneous velocity. The instantaneous acceleration of the satellite is :
(1) $-bv^3(t)$
(2) $-\frac{bv^3}{M(t)}$ [Correct]
(3) $-\frac{2bv^3}{M(t)}$
(4) $-\frac{bv^3}{2M(t)}$
Show Answer
Answer: (2)
Solution
Thrust $F = -v\frac{dm}{dt} = -bv^3$. $a = \frac{-bv^3}{M(t)}$.
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