Concepts Of Physics MCQ Edition [Volume 1]PhysicsSimple Harmonic Motion
A uniform disc having mass m and radius r is suspended by a wire attached to its centre. If the time period of torsional oscillations is T , determine the torsional constant of the wire.
Options
- A2 ^2 m r^2 T^2
- B8 ^2 m r^2 T^2
- C^2 m r^2 T^2
- D4 ^2 m r^2 T^2
Correct answer
A. 2 ^2 m r^2 T^2
Step-by-step solution
The time period of torsional oscillations is given by: T = 2 I C where I is the moment of inertia of the disc and C is the torsional constant of the wire. The moment of inertia of a uniform disc about an axis passing through its centre and perpendicular to its plane is: I = m r^2 2 Substituting the value of I in the expression for T : T = 2 m r^2 2 C Squaring both sides: T^2 = 4 ^2 ( m r^2 2 C ) T^2 = 2 ^2 m r^2 C Rearranging for C : C = 2 ^2 m r^2 T^2