Two masses 8 kg and 12 kg are connected at the two ends of a light in extensible string that passes over a friction less pulley. Find the acceleration of the masses and tension in the string , when the masses are released
.

Explanation

For block `m_2` `rarr` `m_2` g _ T = `m_2`a …(i)
and for block `m_1` `rarr` T - `m_1`g = `m_1`a …..(ii)
Adding (i) and (ii) , we obtain
(`m_2 - m_1`) g = (`m_2 + m_1)` a
a = (`m_2 - m_1` / `m_2 + m_1`)g
= 12 - 8 / 12 + 8 `xx` 10
= `4 xx 10 / 20 ` = 20 `ms^(-2)`
Substituting value of a in equation (ii), we obtain
T = `m_1`(g + a)
= `8 xx (10 + 2)`
= `8 xx 12 `= 96 N.