First slide

Simple hormonic motion

Question

A heavy brass-sphere is hung from a spiral spring and it executes vertical vibrations with period T. The ball is now immersed in non-viscous liquid with a density one-tenth that of brass. When set into vertical vibrations with the sphere remaining inside the liquid all the time, the period will be

Moderate

A

$(9/10) T$
B

$T \sqrt{(10 / 9)}$
C

$T \sqrt{(9 / 10)}$
D

unchanged

Solution

$We know that T = 2 π \sqrt{(\frac{M}{k})} when the sphere is immersed in liquid, the weiSht i reduced to (1 / 10) th of the original value . So, we can say reduced to (1 / 10) th of the original value . So, we can say spring . Now T_{1} = 2 π \sqrt{(\frac{9 M}{10 k})} = \sqrt{(\frac{9}{10}) [2 π \sqrt{(\frac{M}{k})}]} = \sqrt{(\frac{9}{10}) T}$

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