A rocket of mass $4000 k g$ is set for vertical firing. How much gas must be ejected per second so that the rocket may have initial upwards acceleration of magnitude $19.6 m {/ s}^{2}$ ? [Exhaust speed of fuel $= 980 m / s$ ]

240 k g / s

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80 k g / s

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120 k g / s

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None

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Solution

The correct option is C $120 k g / s$
For upward motion of rocket, thrust force must be greater in magnitude than its weight and net force will be equal to their difference, i.e.,
$U p w a r d t h r u s t - W e i g h t = F_{n e t}$
$- v_{e} \frac{d m}{d t} - m g = m a$
$- \frac{d m}{d t} = \frac{m a + m g}{v_{e}}$

Here, negative sign is implying that mass of gas is decreasing with the passage of time and $v_{e} = 980 m / s$ is the exhaust speed of fuel.
Hence $- \frac{d m}{d t} = \frac{m (a + g)}{v_{e}}$
$- \frac{d m}{d t} = \frac{4000 (19.6 + 9.8)}{980}$
$∴ - \frac{d m}{d t} = 120 k g / s$

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A rocket of mass 4000 kg is set for vertical firing. How much gas must be ejected per second so that the rocket may have initial upwards acceleration of magnitude 19.6 m/s2? [Exhaust speed of fuel =980m/s]

A rocket of mass $4000 k g$ is set for vertical firing. How much gas must be ejected per second so that the rocket may have initial upwards acceleration of magnitude $19.6 m {/ s}^{2}$ ? [Exhaust speed of fuel $= 980 m / s$ ]