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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/√aV(x)=K|x|3∴[K]=[V][x]3=[ML2T−2][L3]=[ML−1T−2]Now time period may depends on T∝(mass)x(amplitude)y(K)z[M0L0T]=[M]x[L]y[ML−1T−2]zEquating powers we get,−2z=1,z=−12y−z=0,y=−12asT∝(amplitude)yT∝(a)−12T∝1√a

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