Radial & Tangential Acceleration for Non Uniform Circular Motion
A particle pl...
Question
A particle placed on top of a smooth sphere of radius 2m slides through a distance of π3m 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
0m/s
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B
5.16m/s
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C
4.16m/s
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D
10m/s
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Solution
The correct option is C4.16m/s
Distance covered on the surface of the sphere =s=π3m ∴ 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=mv2r⇒v=√rgcosθ ⇒v=√2×10×cos30∘=√20×√32 ⇒v=4.16m/s