A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m s⁻¹. To give an initial upward acceleration of 20 m/s², the amount of gas ejected per second to supply the needed thrust will be ( g = 10 m s⁻²) (a) 127.5 kg s⁻¹ (b) 187.5 kg s⁻¹ (c) 185.5 kg s⁻¹ (d) 137.5 kg s⁻¹

Answer: (b). Needed thrust: F = m(g + a) = 5000 × (10 + 20) = 1.5 × 10⁵ N. F = udm/dt ⇒ dm/dt = 1.5 × 10⁵800 dm/dt = 187.5 kg s⁻¹ So the answer is (b).

A 5000 kg rocket is set for vertical firing. The exhaust speed is 800… | NEET 1998 (AIPMT)

Q24NEET 1998 · AIPMTMedium

Impulse & Momentum Conservation

A $5000\text{ kg}$ rocket is set for vertical firing. The exhaust speed is $800\text{ m s}^{-1}$ . To give an initial upward acceleration of $20\text{ m/s}^{2}$ , the amount of gas ejected per second to supply the needed thrust will be ( $g = 10\text{ m s}^{-2}$ )

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Answer: (b)

Needed thrust: $F = m(g + a) = 5000 \times (10 + 20) = 1.5 \times 10^{5}$ N.
$F = u\frac{dm}{dt} \Rightarrow \frac{dm}{dt} = \frac{1.5 \times 10^{5}}{800}$
$\frac{dm}{dt} = 187.5\text{ kg s}^{-1}$
So the answer is (b).

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