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Homework Statement
The descending pulley (disc shaped) shown in the figure have a radius 20 cm and moment of inertia 0.20 kgm^{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 kgm^{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 anticlockwise.
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_1T_2)R=I\alpha \Rightarrow (T_1T_2)(0.2)=(0.2)\alpha \Rightarrow T_1T_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!
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