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

Answer 1

Let,

T= tension of the string

a= common acceleration

$T-m_{1}g=m_{1}a---------\left(1\right)$

$m_{2}g-T=m_{2}a-------\left(2\right)$

$(m_2-m_1)g=(m_1+m_2)a$

$a=\frac{(m_2-m_1)g}{m_1+m_2}$-------- (3)

From (1) and (3)

$T=m_{1}g+m_1\frac{(m_2-m_1)g}{m_1+m_2}$

$T=\frac{m_{2}g}{m_1+m_2}(m_1+m_2+m_2-m_1)$

$T=\frac{2m_1{m}_{2}g}{m_1+m_2}-------\left(4\right)$

Given, $m_1=8kg,m_2=12kg,g=10m/s^2$

(3)=> $a=\frac{12-8}{8+12}\times 10=\frac{4}{20}\times 10=2m{s}^{-2}$

Now, from equation (1)=> T= $m_{1}a+m_{2}g$

T= $8\times 2+8\times 10$

T= 96N