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Consider four objects, all solid spheres. Sphere (A) has radius r and mass m, (B) has radius 2r and mass m, (C) has radius r and mass 2m, and (D) has radius r and mass 3m. All can be placed at the same point on the same inclined plane where they will roll without slipping to the bottom. The answer to the following questions might also be (E), all are the same. (a) Which object has the largest rotational inertia? (b) If released from rest, which object will experience the largest net torque? (c) If released from rest, which object will experience the largest linear acceleration? (d) If allowed to roll down the incline, which object will have the largest speed at the bottom of the incline? (e) If allowed to roll down the incline, which object will reach the bottom of the incline in the shortest time?

Consider four objects, all solid spheres. Sphere (A) has radius r and mass m, (B) has radius 2r and mass m, (C) has radius r and mass 2m, and (D) has radius r and mass 3m. All can be placed at the same point on the same inclined plane where they will roll without slipping to the bottom. The answer to the following questions might also be (E), all are the same.
(a) Which object has the largest rotational inertia?
(b) If released from rest, which object will experience the largest net torque?
(c) If released from rest, which object will experience the largest linear acceleration?
(d) If allowed to roll down the incline, which object will have the largest speed at the bottom of the incline?
(e) If allowed to roll down the incline, which object will reach the bottom of the incline in the shortest time?

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
7 years ago
(a)
The correct option is sphere (B).
Assume that the rotational inertia of sphere about the axis of rotation is given by I , and it rolls down the inclined plane with angle of inclination θ .
The rotational inertia of the sphere is given as:
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(e)
The correct option is sphere (A), sphere (C), and sphere (D).
The time taken to reach the bottom is given as:
t = \frac{d}{v}
From part (c), it is clear that sphere (A), sphere (C), and sphere (D) all have largest speed, and for being the same, the time to reach the bottom must also be the same.


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