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.)

Step-by-step solution

Key Idea Velocity of a rocket at any timet, v=u ( m₀ m )-g t where, u= speed of exhausted gases, m₀= initial mass of the rocket and m= mass of the rocket at time t Given, fuel burned rate, ( d m d t )=100 ~kg / s , u=5 km / s Then, v=5 ( m₀ 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 m₀ . or m₀ m =20 So, v=5 (20) km / s Hence, the correct option is (3).