A sphere of radius r is placed on a concave surface of radius of curvature 5 r, which itself is placed on a horizontal table as shown in fig. (3). When the sphere is displaced from the equilibrium position it describes S.H.M. of period
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a
2π(r/g)1/2
b
4π(r/g)1/2
c
2π(5r/g)1/2
d
2π(6r/g)1/2
answer is B.
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Detailed Solution
Here, restoring force = - M g sin θ Considering the displaced position, we havesinθ=X/(5r−r)=X/4r ∴ Ma=−Mg(x/4r) a=−(g/4r)X so T=2π4rg=4πrg