Question

Two blocks of masses $5kg$ and $2kg$ (see fig) are initially at rest on the floor. They are connected by a light string, passing over a light frictionless pulley. An upward force $F$ is applied on the pulley and maintained constant. Calculate the acceleration $a_1$ and $a_2$ of the $5kg$ and $2kg$ masses, respectively, when $F$ is $110N(g=10m/s^2$)

• A. $a_1=1m{s}^{-2},a_2=17.5m{s}^{-2}$
• B. $a_1=1m{s}^{-2},a_2=0m{s}^{-2}$
• C. $a_1=2m{s}^{-2},a_2=17.5m{s}^{-2}$
• D. $a_1=2m{s}^{-2},a_2=0m{s}^{-2}$

Answer 1

The correct option is A $a_1=1m{s}^{-2},a_2=17.5m{s}^{-2}$

FBD of 5kg body,

$T-50=5a_1\therefore 5=5a_1\Rightarrow a_1=1m/s^2$

FBD of 2kg body,

$T-20=2a_2\Rightarrow a_2=17.5m/s^2$