Question

Two masses $8 \,kg$ and $12 \,kg$ 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. $2 \,m / s ^{2}$ and 90 N
• B. $4\, m / s ^{2}$ and 90 N
• C. $2\, m / s ^{2}$ and 60 N
• D. $4\, m / s ^{2}$ and 99 N

Answer 1

Answer: (A)

Masses connected at the two ends of a light inextensible string are
$m_{1}=8\, kg \,, m_{2}=12\, kg$
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
$m_{2} \,g -m_{1} \,g=\left(m_{1}+m_{2}\right) g$
$\therefore a =\frac{\left(m_{2}-m_{1}\right)}{\left(m_{1}+m_{2}\right)} g\,\,\,...(iii)$
$=\frac{12-8}{12+8} \times 10=2\, m / s ^{2}$
Substituting value of a in Eq. (i), we get
$T =m_{1} \,g+m_{1} \,a$
$=m_{1}(g+a)=8(10+2)=90\, N$