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The cavendish experiment Isaac physics

In 1797, Henry Cavendish measured the density of the Earth to within an amazing 1% of the actual value. His experimental setup consisted of a rod of length L suspended from a wire, with lead spheres on either end, both of mass m. Large lead balls of mass M were placed near each of the small spheres as shown in Figure 1. Due to the force of gravity, the small balls were attracted to the larger ones, turning the rod and so twisting the wire. The wire acted as a torsional pendulum, and so by measuring the angle of deflection he was able to find the torque in the wire, which enabled him to find the attractive force between the larger and smaller spheres.

The torsional pendulum consists of the rod of length L suspended from a wire and spheres of mass m on each end. The pendulum has a period of oscillation T.

Find an expression for the torsion coefficient κ of the string. Assume that the radius of the small spheres are much smaller than the length of the rod and that the rod is light.

Can someone help me please I don’t get this question
Reply 1
There's a rule of thumb for rotational mechanics equations.

you can make the corresponding rotational equation by taking the linear equation and swapping

linear displacement to angular displacement

mass to moment of inertia

the equation for the period of shm in a mass spring system is of course

T=2π sqrt(m/k)

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