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Four solid objects, each with the same mass, are spinning freely with the same angular momentum and the same angular speed. Which object requires the most work to stop it? (A) A solid sphere spinning about a diameter (B) A hollow sphere spinning about a diameter (C) A solid disk spinning about an axis perpendicular to the plane of the disk and through the center. (D) A hoop spinning about an axis along a diameter (E) The work required is the same for all four objects.

Four solid objects, each with the same mass, are spinning freely with the same angular momentum and the same angular speed. Which object requires the most work to stop it?
(A) A solid sphere spinning about a diameter
(B) A hollow sphere spinning about a diameter                                              
(C) A solid disk spinning about an axis perpendicular to the plane of the disk and through the center.
(D) A hoop spinning about an axis along a diameter
(E) The work required is the same for all four objects.

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago
The correct option is (E).
Rotational kinetic energy Krot is defined as,
Krot = ½ L w
Here, angular momentum is L and angular velocity is w.
Work-energy theorem states that, the net work done by the forces acting on a body is equal to the change in the kinetic energy of the body.
So, W = Krot
= ½ L w
Using the equation (W = ½ L w) we observed that, as the four objects, each with same mass, are spinning freely with same angular momentum and same angular speed, therefore the work required is the same for all four objects. Therefore option (E) is correct.

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