A spring block system oscillates simple harmonic motion in the vertical direction. If the time period of a system is $T$ at the surface of the Earth then calculate the time period of a system at the surface of the Moon where gravitational acceleration is $\frac{1}{6}$ of the Earth.

\frac{T}{6}

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\frac{T}{3}

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\frac{T}{\sqrt{6}}

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T

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T \sqrt{6}

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Solution

The correct option is B $T$
Time period of spring block system does not depend upon $g$ therefore if $g$ changes ,time period will remain constant $= T$ ,
$T = 2 π \sqrt{\frac{m}{k}} = 2 π \sqrt{\frac{l}{g}}$
it seems that $T$ depends upon $g$ ,but as the $g$ changes , $l$ will also change and the ratio $\frac{l}{g}$ will remain constant.

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A spring block system oscillates simple harmonic motion in the vertical direction. If the time period of a system is T at the surface of the Earth then calculate the time period of a system at the surface of the Moon where gravitational acceleration is 16 of the Earth.

The correct option is B TTime period of spring block system does not depend upon g therefore if g changes ,time period will remain constant =T, T=2π√mk=2π√lgit seems that T depends upon g ,but as the g changes , l will also change and the ratio lg will remain constant.

A spring block system oscillates simple harmonic motion in the vertical direction. If the time period of a system is $T$ at the surface of the Earth then calculate the time period of a system at the surface of the Moon where gravitational acceleration is $\frac{1}{6}$ of the Earth.