Question

In the figure shown, find the tension $T_1$ (in $N$) in the string. Assume the strings to be inextensible and pulley frictionless.

• A. $2g$
• B. $3g$
• C. $2.5g$
• D. $4g$

Answer 1

The correct option is D $4g$

The given arrangement is shown in the below figure.
Consider $2kg$ and $3kg$ masses as a system and let the acceleration of the entire system is given by $a$.

From the FBD of $10kg$ mass and combined mass of $2kg$ and $3kg$, we get
$\frac{\begin{array}{c}10g-T=10a\\ T-5g=5a\end{array}}{\begin{array}{c}5g=15a\\ a=\frac{g}{3}m/s^2\end{array}}$
From the FBD of $3Kg$ mass we have


From the FBD of $3kg$ mass,
$T_1-3g=3a\Rightarrow T_1=3(g+a)=3(g+\frac{g}{3})$
Thus, $T_1=4gN$