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TOPIC: MOTION IN TWO AND THREE DIMENSION

Number of questions are 265 Select_Question:

Number of questions are 265 Select_Question:

Q1)A 5000 kg rocket is set for firing. The exhaust speed is 800m/s. To give an initial upward acceleration of 20 m/s2, the amount of gas ejected per second to supply the needed thrust will be [AFMC1997]

SOLUTION

In given case mass of rocket is changing with time, but velocity of gases remained constant.

Therefore Thrust=v (dm/dt) -eq(1)

Where dm/dt is rate at which mass of gas is ejected.

Resultant acceleration = Acceleration due to thrust (up) - acceleration due to gravity(down)

20 = a - 10 Or a = 30 is the acceleration produced by thrust

According newton's second law of thrust=(mass)×(acceleration)...(2)

From equation (1) and (2) we get

ma=v ( dm/dt)

5000 × 30=800 ( dm/dt ) On solving equation for (dm/dt)we get

(dm/dt)=187.5 kg/sec

Answer:(c)