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 $$_______________$$

Question

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 $$_______________$$

Infinity Learn · Accepted Answer

[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  $$1$$−$$n2=$$−$$12$$⇒ $$n=3$$

Dimensions of physical quantities

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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 _______________

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Dimensions of physical quantities

Remember concepts with our Masterclasses.

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 _______________

Ready to Test Your Skills?

free study material

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 _______________