Question

In the arrangement shown in the fig. The strings are light and inextensible. The surface over which blocks are placed is smooth. The acceleration and Tension in the string.

• A. $\frac{5}{3}m/s^2,\frac{20}{3}N$
• B. $\frac{5}{6}m/s^2,\frac{10}{3}N$
• C. $\frac{5}{6}m/s^2,\frac{5}{3}N$
• D. $\frac{6}{5}m/s^2,\frac{10}{3}N$

Answer 1

The correct option is A $\frac{5}{3}m/s^2,\frac{20}{3}N$

$\begin{array}{c}\text{So Net force in Honizontal direction}=20\cos {60}^{\circ }\\ =10N\\ \text{So accleration = Net force/Total mass}\\ \begin{array}{c}\end{array}\\ =\left(\frac{10}{4+2}\right)m/s^2\\ =\frac{5}{3}m/s^2\end{array}$

$\text{and now FBD of}2kg\text{Block}$

$\begin{array}{c}\text{So from}FBD\\ \begin{array}{cc}10-T_2& =2\times \frac{5}{3}\\ T_2& =10-\frac{10}{3}\\ T_2& =10\times \frac{2}{3}\\ T_2& =\frac{20}{3}N\end{array}\end{array}$