JEE MAIN - Physics (2021 - 26th August Morning Shift - No. 17)
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/s2]
6.0 $$\times$$ 102 kg s$$-$$1
500 kg s$$-$$1
10 kg s$$-$$1
60 kg s$$-$$1
Explanation
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$${F_{thrust}} = \left( {{{dm} \over {dt}}.{V_{rel}}} \right)$$
$$\left( {{{dm} \over {dt}}{V_{rel}} - mg} \right) = ma$$
$$ \Rightarrow \left( {{{dm} \over {dt}}} \right) \times 500 - {10^3} \times 10 = {10^3} \times 20$$
$${{dm} \over {dt}}$$ = (60 kg /s)
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