Two masses 8 kg and 12 kg are connected at the two ends of a light ine

1.	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 the acceleration of the masses and the tension in the string when the masses are released.
Answer» Let m₁ = 8 kg and m₂ = 12 kg Let T be the tension in the string, and the acceleration with which system moves is 'a'. For mass, m₁, m₁a = T - M₁g or, 8a = T - 8 x 9.8 ....(i) For mass m₂, m₂a = m₂g - T ⇒ 12a = 12 x 9.8 - T ....(ii) Adding equations (i) and (ii), we get (8 + 12)a = T - 8 x 9.8 + 12 x 9.8 - T 20a = 4 x 9.8 ⇒ a = {4 x 9.8}/{20} = 0.69 ms^-2 From equation (i) we get, T = 8 x 0.69 + 8 x 9.8 = 83.92 N

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 the acceleration of the masses and the tension in the string when the masses are released.

Answer»

Let m₁ = 8 kg and m₂ = 12 kg

Let T be the tension in the string, and the acceleration with which system moves is 'a'.

For mass, m₁, m₁a = T - M₁g

or, 8a = T - 8 x 9.8 ....(i)

For mass m₂, m₂a = m₂g - T

⇒ 12a = 12 x 9.8 - T ....(ii)

Adding equations (i) and (ii), we get

(8 + 12)a = T - 8 x 9.8 + 12 x 9.8 - T

20a = 4 x 9.8

⇒ a = {4 x 9.8}/{20} = 0.69 ms^-2

From equation (i) we get,

T = 8 x 0.69 + 8 x 9.8 = 83.92 N