In the figure shown, friction coefficient between the solid sphere and the incline is μ. The center of the sphere is given an initial upward velocity at t = 0, as shown, without imparting any initial angular velocity.Then, which of the following statement(s) is/are true?

Engineering

Physics

Rolling

Question

Pure rolling will definitely begin before the sphere reaches the highest point and the sphere will continue to roll purely after that, even while coming down.

Pure rolling will definitely begin before the sphere reaches the highest point but the sphere will continue to roll purely after that (even while coming down) only if μ is greater than a certain value.

The sphere cannot roll purely while moving up the incline.

The sphere will be rolling purely while coming down if μ > (2tanα)/7

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$μ = \frac{\tan α}{(\frac{{mr}^{2}}{I} + 1)}$