Question

Calculate the acceleration (in $m/s^2$) of the mass $12kg$ shown in the set up of fig. Also calculate the tension in the string connecting the $12kg$ mass. The string is weightless and inextensible, the pulleys are weightless and frictionless.

• A. $\frac{9}{10},\frac{56g}{5}N$
• B. $\frac{2g}{7},\frac{30g}{7}N$
• C. $\frac{10}{g},\frac{5}{56g}N$
• D. $\frac{9}{14},\frac{5}{56g}N$

Answer 1

The correct option is B $\frac{2g}{7},\frac{30g}{7}N$

FBD of $4kg$ mass
$T-2g=4\left(2a\right)$ ...(1)
$12g-2T=12a$ ...(2)
$\Rightarrow 12g-2(8a+2g)=12a\Rightarrow 28a=8g$
$\Rightarrow a=\frac{2g}{7}$ ....(3)
from equation (1) and (3) $T=\frac{30g}{7}$