Discussion Forum

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  $\frac{1}{20}^{th}$  of its initial mass, is [Assume initial speed  to be zero and ignored gravitational and viscous forces]

Answer:

Explanation:

 Key idea    Velocity ofa rocket at any time t.

    $v= u\left(\frac{m_{0}}{m}\right) -gt$

 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 $(\frac{dm}{dt}) $=100 kg/s, u=5 km/s

 Then, $v= 5ln( \frac{m_{0}}{m})-gt$

 As, it is given that the gravitational force is ignored and mass of rocket is reduced to $\frac{1}{20}$ th of 

it's initial mass  i.e, m= $\frac{1}{20}  m_{0}$

 or    $\frac{m_{0}}{m}=20$

so, v=5 ln(20) km/s

 Hence, the correct option  is (c)