SATHEE: Rotation 3 Question 17

Rotation 3 Question 17

25. A ring of mass $0.3 k g$ and radius $0.1 m$ and a solid cylinder of mass $0.4 k g$ and of the same radius are given the same kinetic energy and released simultaneously on a flat horizontal surface such that they begin to roll as soon as released towards a wall which is at the same distance from the ring and the cylinder. The rolling friction in both cases is negligible. The cylinder will reach the wall first.

$(1989, 2 M)$

Integer Answer Type Question

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Solution:

In case of ring, $\frac{K_{R}}{K_{T}} = 1$ (pure rolling)

$\begin{array}{ll} or & K_{R} = K_{T} = \frac{K}{2} \\ ∴ & \frac{1}{2} (0.3) v_{1}^{2} = \frac{K}{2} \end{array}$

In case of disc, $\frac{K_{R}}{K_{T}} = \frac{1}{2}$ or $K_{T} = \frac{2}{3} K$

$∴ \frac{1}{2} (0.4) v_{2}^{2} = \frac{2}{3} K$

Soving this equation we get, $h = 0.75 m$ .

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Rotation 3 Question 17

Integer Answer Type Question

Solution:

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