Question

∆. The acceleration in the rocket at any instant is proportional to the nth power of the velocity of the expelled gases. Where the value of n must be?

(a) :  -1

(b) :  1

(c) :  2

(d) :  -2

(e) :  none​

Answer 1

The ‘value’ of n must be one.

Option: (b)

Explanation:  

• If the gases is expelled at velocity v, then the rate of change in linear momentum is equal to mv where m is the ‘mass of the gases’.  

• Now the ‘equal and opposite force’ is experienced on the rocket. If the force experience by a rocket of mass M is F then the acceleration is $M \times a$.  

• Now the forces are equal and opposite hence by using the two equation, $F=m v \text { or } M \times a=m \times v$. Hence from this equation the acceleration is ‘directly proportional to the first power’ of velocity.

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Answer 2

Answer:

B) 1.

Explanation:

The correct answer is 1. At an instant, the acceleration of a rocket is proportional to the nth power of the velocity of exhaust gases. The value of n here is 1. If the gases are expelled at velocity v, then the rate of change in linear momentum is equal to mv where m is the mass of the gases.