Question

Two marbles of identical mass are rolling around a circular track. Marble A is rolling at 12 m/s. Marble B is rolling at 6 m/s. The centripetal force acting on marble A is:

(a) One-fourth as much as the centripetal force acting on marble B.
(b) Twice as much as the centripetal force acting on marble B.
(c) Four times as much as the centripetal force acting on marble B.
(d) Half as much as the centripetal force acting on marble B.
(e) Twelve times as much as the centripetal force acting on marble B.

Answer 1

The centripetal force on Marble A is four times as much as on Marble B because the centripetal force is proportional to the square of the velocity, and Marble A's velocity is twice that of Marble B. Hence, option (c) is correct.

Step-by-step explanation:

The question relates to the concept of centripetal force in a uniform circular motion.

To find the ratio of the centripetal forces on two marbles rolling at different speeds in a circular track, we can use the formula: Fc = m(v2/r).

Since the marbles are of identical mass and presumably moving along the same radii in the circular track, the centripetal force is directly proportional to the square of the velocity (v2).

For Marble A, rolling at 12 m/s, we calculate its centripetal force as proportional to (122) = 144.

For Marble B, rolling at 6 m/s, its centripetal force is proportional to (62) = 36.

Comparing these proportions tells us that the centripetal force on Marble A is 144/36 or four times the centripetal force on Marble B.

Therefore, the correct answer is: (c) Four times as much as the centripetal force acting on Marble B.