Question

Two blocks of masses $5\text{kg}$ and $2\text{kg}$ (see fig.) are initially at rest on the floor. They are connected by a light inextensible 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 $5\text{kg}$ and $2\text{kg}$ masses, respectively, when $F$ is $110\text{N}(g=10{\text{m/s}}^{-2})$

• A. $a_1=1{\text{ms}}^{-2},a_2=17.5{\text{ms}}^{-2}$
  
• B. $a_1=1{\text{ms}}^{-2},a_2=0$
• C. $a_1=2{\text{ms}}^{-2},a_2=17.5{\text{ms}}^{-2}$
• D. $a_1=2{\text{ms}}^{-2},a_2=0$

Answer 1

The correct option is A $a_1=1{\text{ms}}^{-2},a_2=17.5{\text{ms}}^{-2}$


We calculate for both blocks, at the very instant when force 110 N is being applied. So, for both blocks contact from ground will be broken & value of normal reaction =0, in the FBD.

For $5\text{kg}$
$T-5g=5a_1$
$\Rightarrow 55-50=5a_1$
$\Rightarrow a_1=1{\text{m/s}}^2$
For $2\text{kg}$
$\Rightarrow 55-2g=2a_2$
$\Rightarrow 55-20=2a_2$
$\Rightarrow a_2=17.5{\text{m/s}}^2$