A solid sphere rolls without slipping on an inclined plane at an angle θ. The ratio of total kinetic energy to its rotational kinetic energy is (a) 7/2 (b) 5/2 (c) 7/3 (d) 5/4

Answer: (a). Solid sphere: Krot = 1/5mv², Ktrans = 1/2mv², so Ktotal = 7/10mv². KtotalKrot = (7/10)/(1/5) = 7/2 So the answer is (a) 7/2.

A solid sphere rolls without slipping on an inclined plane at an… | MHT CET 2023 (9 May, Shift 1)

Q36MHT CET 2023 · 9 MAY · SHIFT 1Easy

Rolling Motion

A solid sphere rolls without slipping on an inclined plane at an angle $\theta$ . The ratio of total kinetic energy to its rotational kinetic energy is

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Answer: (a)

Solid sphere: $K_{rot} = \frac{1}{5}mv^2$ , $K_{trans} = \frac{1}{2}mv^2$ , so $K_{total} = \frac{7}{10}mv^2$ .
$\frac{K_{total}}{K_{rot}} = \frac{7/10}{1/5} = \frac{7}{2}$
So the answer is (a) $\frac{7}{2}$ .

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