Question

At a certain instant of time the mass of a rocket going up vertically is $100$ kg. If its is ejecting $5$ kg of gas per second at a speed of $400$ m/s, the acceleration of the rocket would be (taking $g=10m/s^2$)

• A. $20m/s^2$
• B. $10m/s^2$
• C. $2m/s^2$
• D. $1m/s^2$

Answer 1

The correct option is B $10m/s^2$

Force acting upward on the rocket $F=\frac{dP}{dt}=\frac{d}{dt}mv=v\frac{dm}{dt}=5\times 400=2000N$

Gravitational force acting down$=Mg=100\times 10=1000N$

Hence, net force $F_{net}=2000-1000=1000N$ upward

$a=\frac{F_{net}}{M}=\frac{1000}{100}$

$⟹a=10m/s^2$

Answer-(B)