Question

Two block $A$ and $B$ of masses $10kg$, respectively, connected by a light string are placed on the smooth horizontal table. The middle point of string is pulled through another light string by applying a force $F$. Due to application of force. both blocks begin to move with same magnitude of acceleration $\frac{100}{\sqrt{3}}m/s^2$. Find the value of $F$

• A. $2000N$
• B. $1000\sqrt{3}N$
• C. $1000N$
• D. $50N$

Answer 1

The correct option is C $1000N$

Correct option is $\left(C\right)$

$\begin{array}{cc}\text{On}B:T_B& =\text{Ma}\\ & =20\times \frac{100}{\sqrt{3}}\\ & =\frac{2000N}{\sqrt{3}}\\ \text{On}A;T_A& =M_{h}a\\ & =10\times \frac{100}{\sqrt{3}}\\ & =\frac{1000}{\sqrt{3}}N\end{array}$

At the middle point: $T_B\sin \theta =T_A$

$\begin{array}{c}\frac{2000\sin \theta }{\sqrt{3}}=\frac{1000}{\sqrt{3}}\\ \theta ={30}^{\circ }\end{array}$

Hence; $T_B\cos \theta =F$

$\frac{2000}{\sqrt{3}}\times \sqrt{3/2}=F$

$1000N=F$