Question

Two masses $8kg$ and $12kg$ are connected at the two ends of a light inextensible string that goes aver a frictionless pulley. The acceleration of the masses and the tension in the string when the masses are released, are respectively

• A. $2m/s^2$ and 90 N
• B. $4m/s^2$ and 90 N
• C. $2m/s^2$ and 60 N
• D. $4m/s^2$ and 99 N

Answer 1

Answer: (A)

Masses connected at the two ends of a light inextensible string are
$m_1=8kg,m_2=12kg$
Let $T$ be the tension in the string and masses moves with an acceleration a when masses are released.
For mass $m_1$
$T-m_{1}g=m_{1}a...(i)$
For mass $m_2$
$m_{2}g-T=m_{2}a...(ii)$
Adding Eqs. (i) and (ii), we get
$m_{2}g-m_{1}g=\left(m_1+m_2\right)g$
$\therefore a=\frac{\left(m_2-m_1\right)}{\left(m_1+m_2\right)}g...(iii)$
$=\frac{12-8}{12+8}\times 10=2m/s^2$
Substituting value of a in Eq. (i), we get
$T=m_{1}g+m_{1}a$
$=m_1(g+a)=8(10+2)=90N$