Question

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights ʰₛₚₕ and ʰcᵧₗ on the incline. The ratio (ʰₛₚₕ)/ (ʰcᵧₗ) is given by:
(A) 1 (B) 4/5
(C) 2/√5
(D) 14/15

Answer 1

Answer:

Here is your answer mate

Answer 2

The two climb maximum heights ʰₛₚₕ and ʰcᵧₗ on the incline. The ratio (ʰₛₚₕ)/ (ʰcᵧₗ) is given by h (sph) / h (cyl) = 14 / 15

Option (D) is correct.

Explanation:

For solid sphere :

1/2 mv^2 + 1/2 . 2/5 mR^2 . v^2 / R^2 = mgh (sph)

For solid cylinder:

1/2 mv^2 + 1/2 . 1/5 mR^2 . v^2 / R^2 = mgh (cyl)

Now taking the ratio:

h (sph) / h (cyl) = 7 / 5 ÷ 3 / 2

h (sph) / h (cyl) = 14 / 15

Thus the two climb maximum heights ʰₛₚₕ and ʰcᵧₗ on the incline. The ratio (ʰₛₚₕ)/ (ʰcᵧₗ) is given by h (sph) / h (cyl) = 14 / 15