The pulley shown in figure (10-E8) has a radius 10 cm and moment of inertia 0.5 kg-m2 about its axis. Assuming the inclined planes to be frictionless, calculate the acceleration of the 4.0 kg block.

The acceleration of the 4kg block is given as

Given

The radius of the pulley is given as 10 cm, the inertia 0.5 and the mass of the blocks are given as 2 kg and 4 kg.

Formula Used

The formula used to find the acceleration of the mass pulled/pushed is determined by the second law of Newton when the Force/Tension applied is equivalent to the product of mass and acceleration

where

is the force of the mass in terms of tension, is the acceleration and m is the mass of the block.

Explanation

The mass and tension relationship of the 4 kg block is given as

The tension and the mass of the 4 kg block is denoted as and respectively.

The mass and tension relationship of the 2 kg block is given as

The tension and the mass of the 2 kg block is denoted as and respectively.

The difference in their tension is given in terms of moment of Inertia

Adding all the three equations we get the value of the acceleration of the blocks made the 4 kg block is

Putting the values of the masses, radius and gravity as , we get the value of acceleration as