The rate of mass of the gas emitted from the rear of a rocket is initially `0.1 kg//s`. If the speed of the gas relative to the rocket is `50 m//s` and the mass of the rocket is `2 kg` , then the acceleration of the rocket in `m//s^(2)` is

Options

A. 5
B. 5.2
C. 2.5
D. 25

Answer

C

Explanation

`(dm)/(dt) = 0.1 kg// sec , v_(r) = 50m//s : m = 2kg`
Mass of rocket = 2kg
Law of conservation of momentum - Mv = cosnstant `rArr - v (dm)/(dt) + M (dv)/(dt) = 0`
`therefore (dv)/(dt) = (50 xx 0.1)/(2) = 2.5m//s^(2)`