Laws Of Motion Question 416
Question: If M is mass of rocket, r is rate of ejection of gases with respect to rocket, then acceleration of the rocket $ \frac{dv}{dt} $ is equal to
Options:
A) $ \frac{ru}{(m-rt)} $
B) $ \frac{(m-rt)}{ru} $
C) $ \frac{ru}{(m+rt)} $
D) $ \frac{ru}{m} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Here, initial mass of rocket = M. $ \frac{dm}{dt}=r $
Relative velocity of gases w.r.t. rocket = v then acceleration of the rocket,
$ a=\frac{F}{m}=\frac{u(dm/dt)}{( M-\frac{dm}{dt}\times t )}=\frac{ur}{M-rt} $
