A body of mass m hung at one end of the spring executes SHM. where K is the force constant of the spring. prove that the relation given below is incorrect, alsoderive correct relation.T= 2πm/K (do it in paper )

A body of mass m hung at one end of the spring executes SHM. where K i

1.	A body of mass m hung at one end of the spring executes SHM. where K is the force constant of the spring. prove that the relation given below is incorrect, alsoderive correct relation.T= 2πm/K (do it in paper )
Answer» Explanation:A body of mass m hung at one end of the spring executes simple harmonic motion . The force constant of a spring is k while its period of vibration is T. Prove by dimensional method that the equation T=2πm/k is correct. ... As the DIMENSIONS of two sides are not equal , hence the equation is incorrectCmk−−−√ Solution : The GIVEN equation is T=2πmk Taking the dimensions of both sides, we have [T]=[M][ML0T−2]=T2 As the dimensions of two sides are not equal , hence the equation is incorrect. Let the correct relation be T=Cmakb,whereC is constant. Equating the dimensions of both sides , we get [T]=[M]a[MT−2]b or [M0L0T]=[Ma+bL0T−2b] COMPARING the POWERS of M,L, and T on both sides , we get a+b=0and−2b=1. Therefore , b=−12anda=12 :. T=Cm−1/2k−1/2=Cmk−−−√ This is the correct equation

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A body of mass m hung at one end of the spring executes SHM. where K is the force constant of the spring. prove that the relation given below is incorrect, alsoderive correct relation.T= 2πm/K​ (do it in paper )​

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A body of mass m hung at one end of the spring executes SHM. where K is the force constant of the spring. prove that the relation given below is incorrect, alsoderive correct relation.T= 2πm/K (do it in paper )