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A smooth hemisphere is kept fixed on ...

A smooth hemisphere is kept fixed on a horizontal floor . A small block f mass m is kept on the tip of hemisphere . Block is slightly pushed and it is found that block leaves contact with the spherical surface when radius through the block makes and angle `theta ` with the vartical . Calculate `theta ` .

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AI Generated Solution

To solve the problem of finding the angle \( \theta \) at which the block leaves contact with the hemisphere, we will follow these steps: ### Step 1: Understand the Forces Acting on the Block When the block is at an angle \( \theta \) with the vertical, two forces act on it: - The weight of the block \( mg \) acting downwards. - The normal force \( N \) acting perpendicular to the surface of the hemisphere. ### Step 2: Apply Newton's Second Law in the Radial Direction ...
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