Question

In the experiment, you will study an oscillator called a "torsion pendulum." In this case, the restoring "force" is the torsion constant of the wire that suspends the weight X and the inertial term is the rotational inertia of the suspended mass. You will compare the periods of a suspended sphere and of a suspended cube. The rotational inertia of a sphere is Is = 110msD2, where ms is the mass of the sphere and D is its diameter. The rotational inertia of a cube is Ic = 16mcS2, where mc is the mass of the cube and S is the length of its side. If the cube and the sphere are suspended from the same wire, what is the expected ratio of their periods, Tc/Ts? Assume that D = S,

Answer 1

Answer:

$\dfrac{T_c}{T_s}= 0.381$

Explanation:

Given that

For sphere

Is = 110msD²

For cube

Ic = 16mcS²

D= S

We know that time period of torsion pendulum is directly proportional to the square root of  the rotational inertia.

$T=2\pi \sqrt{\dfrac{I}{K}}$

$\dfrac{T_s}{T_c}= \sqrt{\dfrac{I_s}{I_c}}$

Now by putting the values

$\dfrac{T_s}{T_c}= \sqrt{\dfrac{110}{16}}$

$\dfrac{T_s}{T_c}= 2.62$

$\dfrac{T_c}{T_s}= 0.381$