Question

Two masses $8 \,kg$ and $12 \,kg$ are connected at the two ends of a string that goes over a frictionless pulley. Calculate the acceleration of the masses and the tension in the string. Take $g = 10 \,m/s^2$

• A. $8\, m/s^2$ , $144 \,N$
• B. $4\, m/s^2$ , $112 \,N$
• C. $6\, m/s^2$ , $128 \,N$
• D. $2\, m/s^2$ , $96 \,N$

Answer 1

Answer: (D)

$2\, m/s^2$ , $96 \,N$

Answer 2

Equations of motion are $m_{1}a=T-m_{1}g$ and $m_{2}a=m_{2}g-T$ $\Rightarrow 8a=T-8g \dots(i)$ $12a=12g-T \dots(ii)$ From Eqs. (i) and (ii), we get $a=\frac{g}{5}=2 m/s^{2}$ Substituting the value of $a$ in E $(i)$ we get $T=96\,N$