Question

rotational dynamics question (easy one)

Answer 1

is it (a)?

Answer 2

(c) is the correct answer.....velocity and acceleration of a system of particles depends only on the net force applied on it but not on its point of application......therefore no matter at which point force is applied,the center of mass will acquire the same velocity.

Answer 3

As stated just above, (c) is the correct answer, thanks to Newton's 2nd law of motion.

Answer 4

So, the speed of the centre of mass doesn't depend whether it's moving linearly or staying in one place?

Answer 5

I would write:
"So, the speed of the centre of mass doesn't depend whether the \(\color{blue} {system}\) is moving linearly or \(\color{blue} {rotating}\) ?"

The interesting thing is that this problem, in spite of its appearance, is precisely \(\color{blue} {not}\) a rotational dynamics question.

Answer 6

I agree that the correct answer is c.

It is worth noting that the question specifies that the force acts for the same time delta t in both cases.
That means that the system acquires the same total momentum Fdt in each case.
In case b however, the momentum is acquired by the top mass alone, initially, and so it will move at twice the speed as in case a.
This in turn implies that more energy is imparted to the system in case b.
The extra energy goes into the rotational motion of the system in case b, which is zero in case a, while the kinetic energy of the centre of mass is of course the same in both cases.