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9 June, 07:56

A small light cylinder and a large heavy cylinder are released at the same time and roll down a ramp without slipping. Which one reaches the bottom first?

A. Small cylinder

B. Large cylinder

C. Both reach the bottom at the same time.

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  1. 9 June, 09:47
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    C. Both reach the bottom at the same time.

    Explanation:

    For a rolling object down an inclined plane, the acceleration is given below

    a = g sinθ / (1 + k² / r²)

    θ is angle of inclination, k is radius of gyration, r is radius of the cylinder

    For cylindrical object

    k² / r² = 1/2

    acceleration = g sinθ / (1 + 1/2)

    = 2 g sinθ / 3

    Since it does not depend upon either mass or radius, acceleration of both the cylinder will be equal. Hence they will reach the bottom simultaneously.
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