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A solid sphere rolls on a surface with translational velocity v. To climb an incline continuing to roll without slipping, the minimum v needed to rise through a height h is

Asked in JEE Main Online 2012 · Rolling on an incline

• (1) √2gh
• (2) √(7gh)/5
• (3) √(7gh)/2
• (4) √(10gh)/7

Step-by-step solution

Why the other options are wrong

• (1) Comes from equating 1/2 Mv²=Mgh (ignoring rotation).
• (2) Comes from using 5/7 instead of (10)/7.
• (3) Comes from a factor slip inverting the (10)/7.

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