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(a) A rocket set for vertical firing wei...

(a) A rocket set for vertical firing weighs `50kg` and contains `450kg` of fuel. It can have a maximum exhaust velocity of `2km//s`. What should be its minimum rate of fuel consumption
(i) to just lift off the launching pad?
(ii) to give it an initial acceleration of `20m//s^2`?
(b) What will be the speed of the rocket when the rate of consumption of fuel is `10kg//s` after whole of the fuel is consumed? (Take `g=9.8m//s^2`)

A

2.5 kg/s

B

10 kg/s

C

5 kg/s

D

20 kg/s

Text Solution

Verified by Experts

The correct Answer is:
A
Total mass `= 500 kg, u= 2xx10^(3)m//s`
To lift the rocket off the launching pad, the thrust required
`=u (dm)/(dt) = mg`
`therefore` Rate of fuel consumption,
`(dm)/(dt)= (mg)/(u)= (500xx10)/(2xx10^(3))= 2.5kg//s`
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