Question

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find out the acceleration of the masses and the tension in the string when the masses are released.

Answer 1

Given; m₁ = 12 kg; m₂ = 8kg

T = ?

a = ?

When the masses are released, mass being heavier will move downwards and m₂ will move upwards with the same acceleration.
Now equation of motion for mass m₁,
m₁g – T = m₁a ……………. (1)
and that for m₂,
T – m₂g = m₂a …………….. (2)
On adding equation (1) & (2), we get

or a = 1.96 m/s ²
≈ 2m/s²
From equation (2),
T₂ = m₂g + m₂a
= m₂ (g + a)
= 8 (10 + 2)
= 8 × 12
= 96 N