Question

If force, $F=48N$ is acting on the system as shown in figure, find the tension in string. All surfaces are smooth.
(Take $g=10m/s^2$)

• A. $12N$
• B. $9.6N$
• C. $8.4N$
• D. $5.6N$

Answer 1

The correct option is B $9.6N$

Considering ($4kg+6kg$) as a system and the FBD of the $10kg$ body is given as

Component of force parallel to the plane, $=48\cos {60}^{\circ }=24N$
Since,
$10g\sin {37}^o(=60N)>24N$
System will accelerate down the plane.
Hence, $a=\frac{F_{net}}{m_{total}}=\frac{60-24}{10}=3.6m/s^2$

Let the tension in the string be $T$, considering the FBD of $4kg$

Using Newton's second law,
$4g\sin {37}^o-T=ma=4\times 3.6\Rightarrow T=(4\times 10\times \frac{3}{5})-14.4=9.6N$