A23.0 kg bucket of water is suspended by a very light rope wrapped around a solid uniform cylinder 0.300 m in diameter with mass 13.0 kg. the cylinder pivots on a frictionless axle through its center. the bucket is released from rest at the top of a well and falls 10.5 m to the water.

The tension in the rope is 49.66 N.

Explanation:

Given that,

Mass of bucket m= 23.0 kg

Diameter = 0.300 m

Mass of rope M= 13.0 kg

Height = 10.5 m

Suppose we need to find the tension in the rope while the bucket is falling.

We need to calculate the acceleration

Using balance equation

..(I)

We need to calculate the tension in the rope

Using formula of tension

....(II)

Put the value of T in the equation (I)

Put the value into the formula

Now, put the value of a in equation (II)

Hence, The tension in the rope is 49.66 N.