A light pole of length L is at rest and makes an angle of theta with respect to

Question

A light pole of length L is at rest and makes an angle of theta with respect to the horizontal. The bottom end of the pole is hinged at the floor. A fish of mass m_f hangs at rest from the top end of the pole. A horizontal cable is attached to the pole at a point 2/3L from the bottom of the pole. What is the mass of the fish if the magnitude of the tension in the horizontal cable is 25.0 N and theta = 70.0 degree? SHOW ALL WORK! If the horizontal cable is moved so that it connects to the pole at a point 1/3L from the hinged bottom (but the cable is still horizontal and theta remains unchanged), will the magnitude of the torque exerted on the pole around the hinged bottom by the horizontal cable in the new position increase, decrease, or remain the same? The magnitude of the torque by the cable in the new position will increase. The magnitude of the torque by the cable in the new position will decrease. The magnitude of the torque by the cable in the new position will remain the same.

Explanation / Answer

Taking moment equilibrium from hinge,

m (fish) *g * L cos70 = T * (2/3 L ) * sin70

So m(fish) = T * (2/3) * tan 70 / g

Similarly forthe new position.

m(fish) * g* L cos(70) = T * (1/3 L ) * sin 70

Sinnce mass of fish is not change from the 1 st case, Shifting the cable closer, the cable has to exert the same torque to remain in equilibrium.

T will change i.e tension by 2 times. But as the length is halved from 2/3 L to 1/3 L net torque will be same.

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