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Question

A particle placed on top of a smooth sphere of radius 2 m slides through a distance of π3 m and falls off the sphere. What is the velocity of the particle when it is about to drop off the surface of the sphere?

A
0 m/s
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B
5.16 m/s
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C
4.16 m/s
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D
10 m/s
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Solution

The correct option is C 4.16 m/s

Distance covered on the surface of the sphere =s=π3 m
Angle subtended at the centre of the sphere =θ=sr=π32=π6
The particle makes an angle of 30 with the vertical as it falls off.
FBD of the particle as it falls off:


As the particle falls off, the normal force, N=0
Since N=0, from the free body diagram, we can see that,
mgcosθ=mv2rv=rgcosθ
v=2×10×cos30=20×32
v=4.16 m/s

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