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Question

A particle of mass m begins to slide down a fixed smooth sphere from the top with negligible initial velocity. What is its tangential acceleration when it breaks off the sphere?

A
2g3
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B
5g3
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C
g
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D
g3
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Solution

The correct option is B 5g3
If a particle starts from the top,the speed of the particle will be given by energy conservation law.It is given as
change in the potential energy = gain in kinetic energy
mgR(1cosθ)=12mv2
from force equation now
since it break off at this position so normal force will be zero
mgcosθ=mv2R
now we will use the value from above two equations
mgcosθ=2mg×(1cosθ)
by solving above equation
cosθ=23
now for tangential acceleration as we know that
at=Fmm
at=mgsinθm
at=gsinθ
from above equation
sinθ=53
so tangential acceleration will be
at=53g
at=7.45ms2







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