JEE Main · 2004 · 24 Apr 2004 · Offline · Elasticity & SHM

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

t_{0}

in air. Neglecting frictional force of water and given that the density of the bob is

(\frac{4}{3}) \times 1000 kg / m^{3}

. What relationship between t and

t_{0}

is true?

Answer: (C)

Solution

Swinging in a liquid, the bob feels an upthrust that cuts the effective gravity down to

g_{e f f} = g (1 - \frac{ρ _{f l u i d}}{ρ _{b o b}})

, and the period becomes

T = 2 π \frac{L}{g _{e f f}}

. With the bob four-thirds as dense as water,

\frac{ρ _{w a t er}}{ρ _{b o b}} = \frac{3}{4}

, so

g_{e f f} = \frac{g}{4}

and the period lengthens by

\frac{1}{1/4} = 2

. The time therefore becomes

2 t_{0}

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option