Rotation 3 Question 17
25. A ring of mass $0.3 kg$ and radius $0.1 m$ and a solid cylinder of mass $0.4 kg$ 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)
$$ \begin{array}{ll} \text { or } & K _R=K _T=\frac{K}{2} \\ \therefore & \frac{1}{2}(0.3) v _1^{2}=\frac{K}{2} \end{array} $$
In case of disc, $\frac{K _R}{K _T}=\frac{1}{2}$ or $\quad K _T=\frac{2}{3} K$
$\therefore \quad \frac{1}{2}(0.4) v _2^{2}=\frac{2}{3} K$
Soving this equation we get, $h=0.75 m$.
