A rocket motor consumes 100 kg of fuel per second exhausting it with a speed of 5 km/s. The speed of the rocket when its mass is reduced to `(1^(th))/(20)` of its initial mass, is ( Assume initial speed to be zero and ignored gravitational and viscous forces. )

Options

A. 20 km/s
B. 40 ln (2) km/s
C. 5 ln (20) km/s
D. 10 ln (10) km/s

Answer

C

Explanation

Key Idea Velocity of a rocket at any time t,
`v=u(m_(0)/m)-at`
where, u`=` speed of exhausted gases,
`m_(0)=` initial mass of the rocket
and `m=` mass of the rocket at time t
Given, fuel burned rate, `((dm)/(dt))=100kg//s, u=5 km//s`
Then, `v=5 ln (m_(0)/m)-g t`
As, it is given that the gravitational force is ignored and mass of rocket is reduced to `(1)/(20)` th of it.s initial mass i.e., `m=(1)/(20)m_(0)`.
or `(m-(0))/(m)=20`
So, `v=5ln(20)km//s`
Hence, the correct option is (c).