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Standard XII

Physics

Examples

A rocket whic...

Question

A rocket which is ejecting gas with a speed of $100 m/s$ and the rate of ejection of the gas from the rocket is $800 kg/s$ . If the mass of the rocket is $4000 kg$ , find out the initial acceleration of the rocket. Take $(g = 10 {m/s}^{2})$

8 {m/s}^{2}

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6 {m/s}^{2}

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12 {m/s}^{2}

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10 {m/s}^{2}

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Solution

The correct option is D $10 {m/s}^{2}$
Mass of rocket, $m = 4000 kg$
Relative velocity of gases w.r.t rocket ; $v = 100 m/s$
Rate of ejection of gas, $= 800 kg/s = \frac{d M}{d t}$

As we know,
$v . \frac{d M}{d t} - m g = m a$
$100 \times 800 - 4000 \times 10 = 4000 \times a$
$a = 10 {m/s}^{2}$

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Standard XII Physics

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A rocket which is ejecting gas with a speed of 100 m/s and the rate of ejection of the gas from the rocket is 800 kg/s. If the mass of the rocket is 4000 kg, find out the initial acceleration of the rocket. Take (g=10 m/s2)

The correct option is D 10 m/s2Mass of rocket, m=4000 kg Relative velocity of gases w.r.t rocket ;v=100 m/s Rate of ejection of gas, =800 kg/s=dMdt As we know, v.dMdt−mg=ma 100×800−4000×10=4000×a a=10 m/s2

A rocket which is ejecting gas with a speed of $100 m/s$ and the rate of ejection of the gas from the rocket is $800 kg/s$ . If the mass of the rocket is $4000 kg$ , find out the initial acceleration of the rocket. Take $(g = 10 {m/s}^{2})$

The correct option is D $10 {m/s}^{2}$
Mass of rocket, $m = 4000 kg$
Relative velocity of gases w.r.t rocket ; $v = 100 m/s$
Rate of ejection of gas, $= 800 kg/s = \frac{d M}{d t}$

As we know,
$v . \frac{d M}{d t} - m g = m a$
$100 \times 800 - 4000 \times 10 = 4000 \times a$
$a = 10 {m/s}^{2}$