A pendulum has time period T in air- When it is made to oscillate in water- it acquired a time period T- -2T- The specific gravity of the pendulum bob is equal to2None of these

The correct option is A 2The effective acceleration of a bob in water =g'=g ( 1 d/D ) where d amp; D are the density of water amp; the bob respectivel ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Thermal Expansion

A pendulum ha...

Question

A pendulum has time period T in air. When it is made to oscillate in water, it acquired a time period $T^{'} = \sqrt{2 T}$ . The specific gravity of the pendulum bob is equal to

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 2
The effective acceleration of a bob in water = $g^{'} = g (1 - \frac{d}{D})$ where d & D are the density of water & the bob respectively.
$\frac{D}{d}$ = specific gravity of the bob.
Since the period of oscillation of the bob in air & water are given as
$T = 2 π \sqrt{\frac{l}{g}} & T^{'} = 2 π \sqrt{\frac{l}{g^{'}}} ∴ \frac{T}{T^{'}} = \sqrt{\frac{g^{'}}{g}} = \sqrt{1 - \frac{d}{D}} = \sqrt{1 - \frac{1}{D}}$
Putting $\frac{T}{T^{'}} = \frac{1}{\sqrt{2}}$ , we obtain
$\frac{1}{2} = 1 - \frac{1}{D}$
$\Rightarrow \frac{1}{D} = \frac{1}{2}$
$\Rightarrow D = 2$

Suggest Corrections

Similar questions

Q. A pendulum has time period T in air when it is made to oscillate in water, it acquired a time period

T^{'} = \sqrt{2} T

. The density of the pendulum bob is equal to (density of water =1) :

Q. Consider the following data and choose the correct option.

1.

The time period of a simple pendulum, whose bob is a hollow metallic sphere is

T

2.

The time period of a simple pendulum is

T_{1},

when the bob is filled with sand,

3.

The time period of a simple pendulum is

T_{2},

when it is filled with mercury and

4.

The time period of a simple pendulum is

T_{3},

when it is half-filled with mercury as shown.

Q. A simple pendulum oscillating in air has period

T

. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is

{(\frac{1}{16})}^{t h}

of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is

Q. A simple pendulum with a solid metal bob has a period T. What will be the period of the same pendulum if it is made to oscillate in a non-viscous liquid of density one-tenth of the metal of the bob?

Q. A simple pendulum oscillating in air has period $T.$ The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is $\dfrac{1}{16}~th$ of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is

Join BYJU'S Learning Program

A pendulum has time period T in air. When it is made to oscillate in water, it acquired a time period T′=√2T. The specific gravity of the pendulum bob is equal to

A pendulum has time period T in air. When it is made to oscillate in water, it acquired a time period $T^{'} = \sqrt{2 T}$ . The specific gravity of the pendulum bob is equal to