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Question

A frictionless wire is fixed between A and B inside a sphere of radius R. A bead slips along the wire. The time taken by the bead to slip from A to B will be:

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A
2R/g
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B
gR/gcosθ
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C
2grgcosθ
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D
2gRcosθg
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Solution

The correct option is A 2R/g
When the bead travels from A to B,
AB=2Rcosθ .............. from geometry.
Also, initial velocity is zero and the component of acceleration acting along AB is gcosθ.
Using kinematic equations,
s=ut+12at2
2Rcosθ=12gcosθt2
4Rg=t2
t=2Rg
134396_72274_ans.png

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