Question

Two masses $2kg$ and $3kg$ are attached to the ends of the string passing over a pulley which is fixed at the top. The tension and acceleration in the string in terms of acceleration due to gravity, $g$ are:

• A. $\frac{7}{8}g,\frac{1}{8}g$
• B. $\frac{21}{8}g,\frac{1}{8}g$
• C. $\frac{21}{8}g,\frac{1}{5}g$
• D. $\frac{12}{5}g,\frac{1}{5}g$

Answer 1

Answer: (D)

$\frac{12}{5}g,\frac{1}{5}g$

From FBD,
for $2kg$ mass: $2a=T-2g....\left(1\right)$
for $3kg$ mass: $3a=3g-T....\left(2\right)$
$\left(1\right)+\left(2\right),5a=g\Rightarrow a=\frac{1}{5}g$
put the value in $\left(1\right)$, we will get, $\frac{2}{5}g=T-2g$
or $T=\frac{2}{5}g+2g=\frac{12}{5}g$