- #1

- 3,812

- 92

## Homework Statement

The descending pulley (disc shaped) shown in the figure have a radius 20 cm and moment of inertia 0.20 kg-m

^{2}. The fixed pulley is light and the horizontal plane frictionless. Find the acceleration of the block if its mass is 1.0 kg.

## Homework Equations

## The Attempt at a Solution

The moment of inertia for a disc about its CoM is: ##\frac{MR^2}{2}##. Equating this with 0.2 kg-m

^{2}and substituting R=0.2 m, M=10 kg.

Let T

_{2}and T

_{1}be the tensions in the strings. T

_{2}on the left of disc and T

_{1}on right of disc.

If A is the acceleration of disc, then 2A is the acceleration of disc. Also, let ##\alpha## be the angular acceleration of disc the direction of which is anti-clockwise.

Newton's second law on disc: ##10g-(T_1+T_2)=10A## and for block: ##T_2=2A## (mass of block is 1 kg).

Torque about CM of disc: ##(T_1-T_2)R=I\alpha \Rightarrow (T_1-T_2)(0.2)=(0.2)\alpha \Rightarrow T_1-T_2=\alpha##.

Next is equating the acceleration along the string. The point of contact of string with the disc on the left goes down with an acceleration of ##A+\alpha R##. Hence, ##A+\alpha R=2A##.

I have enough equations but solving these equations gives me a wrong answer.

Any help is appreciated. Thanks!