Question

A rocket has a mass of $100kg$. $90$ %of this is fuel. It ejects fuel vapours at the rate of $1$ kg/sec with a velocity of $500m/sec$ relative to the rocket. It is supposed that the rocket is outside the gravitational field.The initial upthrust on the rocket when it just starts moving upwards is (in $N$)

• A. $500$
  
• B. $0$
  
• C. $200$
  
• D. $300$
  

Answer 1

The correct option is A $500$

Rate of fuel consumption $\frac{dm}{dt}=1$ $kg/s$

Relative velocity of gases w.r.t rocket $v_{rel}=500m/s$

Initial upthrust on the rocket $F=\frac{dm}{dt}{v}_{rel}$

$\therefore$ $F=1\times 500=500$ $N$