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Q.

In the figure shown a block B of mass $m$ can slide on a fixed horizontal smooth plane. A solid sphere A of radius $r$ of the same mass rolls without sliding on the block B. The angular acceleration of the sphere is $\frac{(5 n) g}{9 r}$ , find the value of ‘ $n$ ’.

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Detailed Solution

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The free body diagrams of sphere A and Block B are as shown
Question Image
Applying Newton’s law to block and sphere
F – f = m a …….. (1)
f = $m a_{c m}$ …….. (2)
$f r = \frac{2}{5} m r^{2} α$ …….. (3)
For no slipping, $a = a_{c m} + r α$ …….. (4)
$∴ a = \frac{10 g}{r}$

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