Question:
A small particle of mass \(m\) is released from rest from point A inside a smooth hemispherical bowl as shown in the figure. The ratio \(x\) of magnitude of centripetal force and normal reaction on the particle at any point B varies with \(\theta\) as
A small particle of mass \(m\) is released from rest from point A inside a smooth hemispherical bowl as shown in the figure. The ratio \(x\) of magnitude of centripetal force and normal reaction on the particle at any point B varies with \(\theta\) as
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For circular motion in a bowl, use energy conservation to find speed, then apply Newton's second law in the radial direction to find the normal force.
Updated On: Apr 20, 2026
- A
- B
- C
- D
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The Correct Option is A
Solution and Explanation
\[
h = R \sin \theta
\]
Speed of the particle at point B,
\[
v^2 = 2gh = 2Rg \sin \theta
\]
Centripetal force,
\[
F = \frac{mv^2}{R} = 2mg \sin \theta \qquad \text{...(i)}
\]
Equation of motion gives
\[
N - mg \sin \theta = \frac{mv^2}{R} = 2mg \sin \theta
\]
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