Question

If the same force is applied on two bodies of different masses for the same time, then the change produced in the momentum of two bodies is also the same.
A) true
B) false

Answer 1

Hint:
To check whether this equation is true or false apply Newton's law of motion. And from it check whether the change in momentum is the same or not for different masses at same time.

Complete step-by-step answer:
As we know that according to Newton's second law of motion force is equal to change in momentum per unit time. This can be written as,
⇒ $F = \dfrac{{dp}}{{dt}}$
Where, F is the force applied on the bodies
dp is the change in the momentum
dt is the change in time
Now, let the force is applied for shorter duration of time dt then from above equation we can write,
⇒ $dp = Fdt$ …………(1)
Since the same force is applied on the two bodies of different masses for the same interval of time dt. Then from equation (1), the change in momentum for both the objects are the same.
It means the momenta of the objects are equal before the application of for, then the momenta of the objects are equal after the force is applied and then withdrawn.
Hence we can say that if the same force is applied on the two bodies of different masses for the same time, then the change produced in the momentum of the two bodies is also the same.
Hence (A) option is correct.

Note
Here we should note that although momentum depends on mass, the change in momentum does not depend upon the mass if equal force is applied for the equal interval of time.