Question

In the figure shown, all pulleys are massless and the strings are light and inextensible. Find the tension in the string attached to the block $m$ of mass $10kg$? (All surfaces are smooth and take $g=10m/s^2$ )

• A. $40\text{N}$
• B. $10\text{N}$
• C. $20\text{N}$
• D. $5\text{N}$

Answer 1

The correct option is D $5\text{N}$

The given system can be reframed as shown

FBDs of the pulleys and the block are

From the FBD of the pulley, $P_7:80-2T=m{a}_7\Rightarrow T=40\text{N}$ as pulley is light, $m=0$
Tension in the string connecting block, $\frac{T}{8}=5\text{N}$

Alternate:
Let say $T$ is the tension in the string connecting block and pulley $P_1$
So, from the string constrained the tension on the string where force $F$ is acting will be $16T$
$\therefore$ we have
$F=16T\Rightarrow T=\frac{F}{16}=\frac{80}{16}=5N$
Thus, the value of tension in the string attached to block of mass $m$ is $T=5N$