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 (43) × $$1000$$ $$kg/m3$$. Which relationship between t and $$t0$$ is true?

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 (43) × $$1000$$ $$kg/m3$$. Which relationship between t and $$t0$$ is true?

Infinity Learn · Accepted Answer

∴ $$t0$$ $$=$$ $$2$$$$π$$lgEffective weight of bob inside water,W' $$=$$ mg $$-$$ thrrust $$=$$ Vρ$$g-V$$ρ`g⇒Vρ$$geff=$$ $$V($$ρ$$-$$ρ$$1)g$$, 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 $$=$$ $$11-34($$∵  ρ' $$=$$ $$103kg/m3$$ and ρ $$=$$ $$43$$×$$103kg/m3) ⇒t $$=$$ $$2$$ $$t0$$

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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 (43) × 1000 kg/m3. Which relationship between t and t0 is true?

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