The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is $$t0$$ in air. Neglecting frictional force of water and given that the density of the bob is (4/3) ×$$1000$$ $$kg/m3$$. What relationship between t and $$t0$$ is true [AIEEE $$2004$$]

Question

The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is $$t0$$ in air. Neglecting frictional force of water and given that the density of the bob is (4/3) ×$$1000$$ $$kg/m3$$. What relationship between t and $$t0$$ is true  [AIEEE $$2004$$]

Infinity Learn · Accepted Answer

∵  $$to=2$$ πlgEffective weight of bob inside water,W'$$=mg$$−$$thrust=V$$ρg−Vρ'g⇒Vρ$$geff=V($$ρ−ρ'$$)g$$, where,  ρ$$=$$ Density of bob ⇒$$geff=1$$−ρ'ρ g and  ρ'$$=$$ Density of water∴$$t=2$$ π$$lgeff=2$$ π$$l(1$$−ρ'$$/$$ρ$$)g$$∴$$tt0=11$$−ρ'$$/$$ρ$$=11$$−$$34$$ $$=2$$                      $$($$∵ρ'$$=103kg/m3$$     ρ$$=43$$×$$103kg/m3$$

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The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is t0 in air. Neglecting frictional force of water and given that the density of the bob is (4/3) ×1000 kg/m3. What relationship between t and t0 is true [AIEEE 2004]

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