Question

The initial mass of a rocket is $1000\, kg$. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of $20\, ms ^{-2}$. The gases come out at a relative speed of $500\, ms ^{-1}$ with respect to the rocket :
[Use $g=10\, m / s ^{2}$ ]

• A. $6.0 \times 10^{2}\, kg\, s ^{-1}$
• B. $500 \,kg \,s ^{-1}$
• C. $10 \,kg \,s ^{-1}$
• D. $60\, kg \,s ^{-1}$

Answer 1

Answer: (D)

$F _{\text{ thrust} }=\left(\frac{ dm }{ dt } \cdot V _{\text{rel}}\right)$
$\left(\frac{ dm }{ dt } V _{\text{rel}}- mg \right)= ma$
$\Rightarrow \left(\frac{ dm }{ dt }\right) \times 500-10^{3} \times 10=10^{3} \times 20$
$\frac{ dm }{ dt }=(60 \,kg / s )$