A particle of mass m is executing oscillation about origin on x-axis. Its potential energy is U(x)=K|X|n .If the time period T is function of its mass, amplitude (a) and (K) ; the value of n if T α a−1/2 (K' is a constant) is _______________

[K]=[U][X]n=ML2T−2Ln=ML2−nT−2T∝( mass )X(amp)Y(K)ZM0L0T=[M]X[L]YML2−nT−2Z=MX+ZLY+2Z−nZT−2Z So, −2Z=1or   Z=−12         ................(i)and, X+Z=0 or  X=−Z=12    ...........................(ii) and, Y+2Z−nZ=0 or Y=1−n2[ from (i) and (ii)]  So, T∝(mass)1/2(amp)1−n/2(K)−1/2 Given T∝(amp)−1/2 So  1−n2=−12⇒ n=3