Question

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 1

I = 0.20 kg-m² (Bigger pulley)
r = 10 cm = 0.1 m, smaller pulley is light
mass of the block, m = 2 kg
therefore mg – T = ma      …(1)
 T = Ia/r²                           …(2)
mg = (m + I/r²)a =>(2 × 9.8) / [2 + (0.2/0.01)]=a = 19.6 / 22 = 0.89 m/s²
Therefore, acceleration of the block = 0.89 m/s².