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Standard XII

Physics

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A rocket, wit...

Question

A rocket, with an initial mass of 1000 kg, is launched vertically upwards from rest. The rocket burns fuel at the rate of 10 kg per second. The burnt matter is ejected vertically downwards with a speed of 2000 $m s^{- 1}$ relative to the rocket. If burning stops after one minute. Find the maximum velocity of the rocket. (Take g as at 10 $m s^{- 2}$ .

1000 m/s

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1232.6 m/s

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1500.5 m/s

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850.6 m/s

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Solution

The correct option is A 1232.6 m/s
Answer is B.
Using the velocity $v = u - g t + v, l n (\frac{m_{0}}{m})$
Here $u = 0, t = 60 s, g = 10 m / s^{2}, v = 2000 m / s, m_{0} = 1000 k g$
and $m = 1000 - 10 \times 60 = 400 k g$
We get $v = 0 - 600 + 2000 l n (1000 / 400)$
or $v = 2000 l n 2.5 - 600$
= 200{10 In 2.5 - 3) = 1232.6 m/s
Hence, maximum velocity of the rocket is 1232.6 m/s.

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The correct option is A 1232.6 m/sAnswer is B.Using the velocity v=u−gt+v,ln(m0m)Here u=0,t=60s,g=10m/s2,v=2000m/s,m0=1000kgand m=1000−10×60=400kgWe get v=0−600+2000ln(1000/400)orv=2000ln2.5−600 = 200{10 In 2.5 - 3) = 1232.6 m/sHence, maximum velocity of the rocket is 1232.6 m/s.