Answer:
[tex]32.67 m/s^2[/tex]
Explanation:
27 cm = 0.27 m
As the blocks are hanging on 2 sides of the pulley, their difference in mass would generate a net force toward the heavier side:
Let g = 9.81 m/s2
F = g(2.7 - 1.4) = 9.81*1.3 = 12.753 N
This force would generate a torque at 0.27 m moment arm
T = F*r = 12.753*0.27 = 3.44 Nm
The moment of inertia of the solid disk:
[tex]I = mR^2/2[/tex]
Where m = 0.78 kg is the disk mass and R = 0.27 m is the radius of the disk.
[tex] I = 0.780*27^2/2 = 0.028431 kgm^2[/tex]
So the angular acceleration of the torque is
[tex]\alpha = T/I = 3.44 / 0.028431 = 121 rad/s^2[/tex]
So the linear acceleration is its angular component times radius
[tex]a = \alpha r = 121 * 0.27 = 32.67 m/s^2[/tex]
