Answer:
The magnitude of the acceleration of the stone is 19.87 m/s²
Explanation:
Given;
mass of stone, m = 375 g = 0.375 kg
moment of inertia, I = 0.0125 kg.m²
radius of the pulley, r = 26 cm = 0.26 m
Torque generated by the pulley on the stone is given as;
τ = F x r = Iα
where;
F is applied force on the stone due to its weight
r is the radius of the pulley
I is moment of inertia
α is angular acceleration (rad/s²)
Force, F = mg = 0.375 x 9.8 = 3.675 N
Torque, τ = F x r
τ = 3.675 x 0.26
τ = 0.9555 N.m
τ = Iα
Angular acceleration, α = τ / I
α = 0.9555 / 0.0125
α = 76.44 rad/s²
Finally, determine linear acceleration, a, in m/s²
a = αr
a = 76.44 x 0.26
a = 19.87 m/s²
Therefore, the magnitude of the acceleration of the stone is 19.87 m/s²
