Question

A rod AB of length = 1m and mass m = 2 kg is pinned to a
vertical shaft and a massless string is tied with the shaft at the
lower end of the rod (length of the string is -m) as shown in
figure. If the shaft starts rotating with a constant angular velocity
m = 5 rad/sec. Then find the tension in the string.
5​

Answer 1

The tension in the string is 8 N-m

Explanation:

dt = dF.g

dx = dmxω^2

dτ = xa^2.x

dτ = x^2 ω^2 / tanθ dm

dτ = x^2 ω^2 / tanθ

dτ = x^2 ω^2λ / tanθ

τ = ω^2λ  / tanθ sinθ

After putting the values we get.

τ = 2 x 4^3 / 4^2

τ = 4 x 2 = 8 N-m

Balancing torque against tangent point.

mg x 2/5 + T x 2/5 = τ

8 + 3T / 5 = 8

T = 0

Thus the tension in the string is 8 N-m