5.16 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.

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Answered by

Vishal Baghel | Contributor-Level 10

4 months ago

Given, small mass, m₁ = 8 kg. bigger mass, m₂ = 12 kg

Let T be the tension in the string

The heavier mass will go downward and the lighter mass will go upward.

Applying Newton's 2^nd law,

For mass m_1,T –m₁g = m₁a …… (1)

For mass m₂, m₂g – T = m₂a……. (2)

Adding (1) & (2), we get

(m_{2 -}m₁₎g_{= (}m_{1 +}m₂₎a

a = (m_{2 -}m₁₎g/₍m_{1 +}m_{2) =}4 $* 10 / 20$ = 2 m/s

From equation (1), we get, T = 8 (2 +10) = 96 N

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