TS EAMCET · Physics · Rotational Motion

A solid cylinder of mass $m$ and radius $R$ rolls down an inclined plane of height $30 m$ without slipping. The speed of its centre of mass when the cylinder reaches the bottom is [use $g = 10 m s^{- 2}$ ]

A $10 m s^{- 1}$
B $20 m s^{- 1}$
C $30 m s^{- 1}$
D $40 m s^{- 1}$

Verified Solution

Answer & Solution

Correct Answer

(B) $20 m s^{- 1}$

Step-by-step Solution

Detailed explanation

Work done by friction during pure rolling is zero therefore, we can apply conservation of mechanical energy. In pure rolling ω=vR For a body having rotational and translational kinetic energy,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A solid cylinder of mass m and radius R rolls down an inclined plane of height 30 m without slipping. The speed of its centre of mass when the cylinder reaches the bottom is [use g=10 m s-2]

Step-by-step Solution

A solid cylinder of mass $m$ and radius $R$ rolls down an inclined plane of height $30 m$ without slipping. The speed of its centre of mass when the cylinder reaches the bottom is [use $g = 10 m s^{- 2}$ ]