TOPIC: MOTION IN TWO AND THREE DIMENSION
Number of questions are 265 Select_Question:

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)