Question

Two blocks of masses $5\text{kg}$ and $2\text{kg}$ are connected by a massless string as shown in figure. A vertical force $F$ is applied on the $5\text{kg}$ block. Find the value of $F$ if tension in the string is $40\text{N}$. $(g=10{\text{m/s}}^2)$

• A. $140\text{N}$
• B. $70\text{N}$
• C. $40\text{N}$
• D. $100\text{N}$

Answer 1

The correct option is A $140\text{N}$

By the free body diagram,
It is given that the tention in the string is $T=40\text{N}$, we also know that the whole system will move with acceleration $a$ .

By the free body diagram of the individual block,
For $2kg$ block Writing the force equation
$T-20=2\times a\Rightarrow 40-20=2\times a$
$a=10{\text{m/s}}^2$

By the free body diagram of $5kg$ and the acceleration is same as $a=10{\text{m/s}}^2$
Writing the force equation
$F-T-50=5a$, $F-40-50=5\times 10$,

on solving $F=140\text{N}$
Hence option (a) is the correct answer.