Chapter 1: Q42E (page 462)

A thin metal disk with mass $2.00 x 10^{- 3} k g$ and radius $2.20 c m$ is attached at its centre to a long fibre. The disk, when twisted and released, oscillates with a period of $1.00 s$ . Find the torsion constant of the fibre.

Short Answer

Expert verified

$T h e t o r s i o n c o n s t a n t o f t h e f i b r e i s 1.9 x 10^{- 6}$

Step by step solution

Definition of torsion constant

The ratio of the torque to the angle is called the torsion constant. It is denoted by c. For a rigid body formula for torsion constant is

$c = \frac{4 π^{2} I}{T^{2}}$

Where,

l = Moment of inertia

T = Time period

calculation of torsion constant

Given,

$M = 2 x 10^{- 3} k g T = 1 s R = 2.2 c m$

So, I of metal disc is localid="1668148513836" $= I = \frac{M R^{2}}{2}$

localid="1668148509505" $P u t v a l u e o f M a n d R w e g e t I = 4.84 x 10^{- 7} k g - m^{2} N o w a c c o r d i n g t o f o r m u l a c = \frac{4 π^{2} I}{T^{2}}$

localid="1668148518008" $p u t a l l t h e v a l u e s i n f o r m u l a c = \frac{4 x 3.14 x 3.14 x 4.84 x 10^{- 7}}{1} C = 1.9 x 10^{- 6} S o, v a l u e o f t o r s i o n c o n s t a n t i s 1.9 x 10^{- 6}$

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A thin metal disk with mass $2.00 x 10^{- 3} k g$ and radius $2.20 c m$ is attached at its centre to a long fibre. The disk, when twisted and released, oscillates with a period of $1.00 s$ . Find the torsion constant of the fibre.

Short Answer

Step by step solution

Definition of torsion constant

calculation of torsion constant

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A thin metal disk with mass 2.00x10-3kgand radius2.20cmis attached at its centre to a long fibre. The disk, when twisted and released, oscillates with a period of1.00s. Find the torsion constant of the fibre.

Short Answer

Step by step solution

Definition of torsion constant

calculation of torsion constant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Circular Motion and Gravitation

Fields in Physics

Magnetism

Linear Momentum

Fundamentals of Physics

Study anywhere. Anytime. Across all devices.

A thin metal disk with mass $2.00 x 10^{- 3} k g$ and radius $2.20 c m$ is attached at its centre to a long fibre. The disk, when twisted and released, oscillates with a period of $1.00 s$ . Find the torsion constant of the fibre.