Question

Two masses 7 kg and 12 kg are connected at the two ends of a light inextensible string over a frictionless pulley. Find the acceleration of the masses and the tension in the string, when the masses are released.

Answer 1

The equation of motion for mass $M_1$ : $M_{1}a=T-M_{1}g$ ...(1)

and for mass $M_2$ : $M_{2}a=M_{2}g-T$ ....(2)

$\left(1\right)+\left(2\right)\Rightarrow a(M_1+M_2)=(M_2-M_1)g$

or $a=\frac{(M_2-M_1)g}{M_1+M_2}=\frac{(12-7)\left(10\right)}{7+12}=\left(50/19\right)m/s^2$

From (1), $T=M_1(a+g)=7(50/19+10)=88.42N$