Question

A rocket is launched by the $PSLV$ in which fuel capacity is $500\text{kg}$. The rocket consumes $2\text{kg}$ fuel in $1\text{s}$. Find the time taken by the rocket to consume $300\text{kg}$ fuel.

• A. $150\text{s}$
• B. $300\text{s}$
• C. $100\text{s}$
• D. $50\text{s}$

Answer 1

The correct option is A $150\text{s}$

Given, total mass of fuel $M=500\text{kg}$
and rate of consumption of fuel
$\frac{dM}{dt}=-2\text{kg/s}$
Integrating and taking the limits of fuel from $500\text{kg}$ to $200\text{kg}$ and time from $0$ to $t$
$\Rightarrow {\int }_{500}^{200}dM={\int }_0^t-2\text{kg/s}dt$
$\Rightarrow [M{]}_{500}^{200}=[-2t{]}_0^t$
$\Rightarrow -300=-2t$
or $t=150\text{s}$ is the time taken to consume $300\text{kg}$ fuel.