First slide

Rolling motion

Question

A small sphere I of radius r and mass m rolls without slipping inside a large hemispherical bowl of radius R as shown in figure. The sphere I starts from rest at the top point on the rim of the hemisphere. Find the normal force exerted by small sphere on the hemisphere when it touches the bottom of hemisphere.

Moderate

A

$\frac{10 mg}{7}$
B

$\frac{9 mg}{7}$
C

$\frac{17 mg}{7}$
D

$\frac{3 mg}{7}$

Solution

Velocity on reaching the bottom:
$mg (R - r) = \frac{7}{10} {mv}^{2}$
$\Rightarrow v^{2} = \frac{10}{7} g (R - r)$
$N - mg = \frac{{mv}^{2}}{R - r} \Rightarrow N = \frac{17}{7} mg$

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