Question

A circular cylinder of radius r = 0.385 m which can rotate freely on a horizontal frictionless axle, has a light rope wound around it. The rope passes over a frictionless pulley and it attached to a hanging box of mass m = 0.98 kg.

Options:
a. 0.474 m
b. 0.295 m
c. 0.184 m
d. 0.122 m

Answer 1

To keep the pulley from rotating, a hanging mass of 7.5 kg must be placed on the cord.

Step-by-step explanation:

To calculate the hanging mass needed to keep the pulley from rotating, we need to consider the torque balance.

Torque is the product of force and lever arm length, and it causes an object to rotate.

In this case, the torque exerted by the hanging mass (T1) should balance the torque exerted by the mass on the frictionless plane (T2). The equation for torque is:

Torque = force * lever arm length

For the hanging mass:

T1 = m * g * r1

For the mass on the frictionless plane:

T2 = M * g * r2

Setting T1 equal to T2 and solving for m:

m = (M * r2) / r1

Substituting the given values:

m = (5.0 kg * 30 cm) / 20 cm

m = 7.5 kg