When a given torque is applied to a 1-m long copper wire, the end rotates by 10°. If half the torque were applied to a 2-m long length of the same wire, by what angle would the end rotate?
A)5 degrees.
B)7.1 degrees.
C)10 degrees.
D)14.1 degrees.
E)20 degrees.

Question

Quizplus · Accepted Answer

The angle of rotation is proportional to the torque applied and inversely proportional to the length of the wire. That is,

angle of rotation = (torque / length of wire)

Let T be the torque applied to the 1-m wire, and let θ be the angle of rotation. Then,

θ = T / 1m

Given that θ = 10°, we have

T = θ × 1m = 10 Nm

Now, let T/2 be the torque applied to the 2-m wire. Let θ' be the angle of rotation in this case. Then,

θ' = (T/2) / 2m = T / 4m

Substituting T = 10 Nm, we get

θ' = 10 Nm / 4m = 2.5 degrees × (180/π) ≈ 14.1 degrees

Therefore, the answer is (C) 10 degrees.

When a Given Torque Is Applied to a 1-M Long