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Question

A particle of mass m is executing oscillation about the origin on X-axis. Its potential energy is V(x)=K|x|3. Where K is a positive constant. If the amplitude of oscillation is a, then its time period T is proportional to.

A
1/a
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B
a
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C
a
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D
a3/2
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Solution

The correct option is A 1/a
V(x)=K|x|3
[K]=[V][x]3=[ML2T2][L3]=[ML1T2]
Now time period may depends on
T(mass)x(amplitude)y(K)z
[M0L0T]=[M]x[L]y[ML1T2]z
Equating powers we get,
2z=1,z=12
yz=0,y=12
as
T(amplitude)y
T(a)12
T1a

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