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 $20 \mathrm{~ms}^{-2}$. The gases come out at a relative speed of $500 \mathrm{~ms}^{-1}$ with respect to the rocket :[Use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$]

(D) $60 \mathrm{~kg} \mathrm{~s}^{-1}$

(A) $500 \mathrm{~kg} \mathrm{~s}^{-1}$

(C) $6.0 \times 10^{2} \mathrm{~kg} \mathrm{~s}^{-1}$

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Conservation of Momentum

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) $500 kg s^{- 1}$
(B) $10 kgs^{- 1}$
(C) $6.0 \times 1 0^{2} kg s^{- 1}$
(D) $60 kg s^{- 1}$ ✓ Correct

Answer: (D)

Solution

The escaping gases push the rocket with thrust

v_{rel} \frac{d m}{d t}

, which must support the weight and still provide the acceleration:

v_{rel} \frac{d m}{d t} - m g = ma

\frac{d m}{d t} = \frac{m ( a + g )}{v _{rel}} = \frac{1000 \times ( 20 + 10 )}{500} = 60 kg s^{- 1}

The fuel must be burnt at

60

kg per second.

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Single correct option

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