The initial mass of a rocket is 1000kg . Calculate at what rate the...

The initial mass of a rocket is $1000kg$ . 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:

\left[\text{Use}g = 10m{s}^{- 2}\right]$

Options

A $10kg{s}^{- 1}$
B $60kg{s}^{- 1}$
C $500kg{s}^{- 1}$
D $6 . 0 \times {10}^{2}kg{s}^{- 1}$

Correct answer

B. $60kg{s}^{- 1}$

Step-by-step solution

Here we are applying the equation,& ${F}_{r} - mg = ma$

From Newton's second law,~ ${F}_{r} = \dfrac{dm}{dt}{v}_{r}⇒ \dfrac{dm}{dt}{v}_{r} = mg + ma$

Put the given values in the above equations,~

$⇒ \dfrac{dm}{dt}500 = 1000 ( 10 + 20 )⇒ \dfrac{dm}{dt} = 60kgs^{- 1}$ .

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