A torsional pendulum comprises a solid disc attached at its centre to a thin wire ( = 2.4 10⁻⁵ ^ C ⁻¹ ). Determine the percentage change in the time period between peak winter ( 5^ C ) and peak summer ( 45^ C ).

Step-by-step solution

The time period of a torsional pendulum 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 torsional constant of a cylindrical wire is given by: C = r^4 2L where is the shear modulus, r is the radius, and L is the length of the wire. When the temperature increases by T , the dimensions of the wire change due to thermal expansion. The new radius and length become: r' = r(1 + T) L' = L(1 + T) The new torsional constant C' is: C' = (r')^4 2L' = r^4 (1 +