Q. 345.0( 1 Vote )

A string is wrapped on a wheel of moment of inertia 0.20 kg-m2 and radius 10 cm and goes through a light pulley to support a block of mass 2.0 kg as shown in figure (10-E5). Find the acceleration of the block.



Answer :

The acceleration of the block is given as


Given


The moment of the inertia of the wheel is given as 0.20 and a radius of 10 cm to support/hang a block of 2 kg mass.


Formula Used


The formula used to find the torque applied on the pulley due to the masses are described below as the product of moment of Inertia and angular acceleration:



where


is the torque of the pulley, is the angular acceleration and I is the moment of Inertia of the pulley


Explanation


The tension applied by the block on the string is given as



The torque of the pulley is given as



Hence, making the moment of Inertia of the pulley as



Now calculating the acceleration in terms of angular acceleration is





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