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Question

A spherical ball of radius 5.5 cm is oscillating in a hemispherical bowl. If the time taken to complete one oscillation by the ball is π2s, then find the radius of hemispherical bowl.

A
68 cm
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B
60 cm
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C
58 cm
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D
32 cm
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Solution

The correct option is A 68 cm
Given,
Radius of spherical ball r=5.5 cm=0.055 m
The oscillation of small spherical ball is analogous to the oscillation of a simple pendulum bob with length of string as, l=Rr

Let R be the radius of hemispherical bowl
Hence time period of oscillation is,
T=2πlg
T=2πRrg
Given, T=π2 s
Hence on equating both,
π2=2πR0.05510
R0.05510=116
R=1016+0.055
R=0.68 m=68 cm

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