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// v, v_(gas)=50 m//s`
Mass of the rocekt =2kg. Mv = constant
`-v(dM)/(dt)+m(dv)/(dt)=0 :. (dv)/(dt)=(1)/(M)v(dM)/(dt)`
`rArr` Acceleration `=(1)/(2) xx50xx0.1 =2.5 m//s^(2)`