Ncert Exercises & Solutions

Q. 40 There are four forces acting at a point P produced by strings as shown in the figure. Which is at rest? Find the forces $F_{1} and F_{2}$ .

Hint: Net force on at point p is zero.

Step 1: Resolve the forces into rectangular components and find

F_{1} and F_{2}

for equilibrium.

Consider the adjacent diagram, in which forces are resolved.

On resolving forces into rectangular components.
We get, equilibrium forces

(F_{1} + \frac{1}{\sqrt{2}}) N

are equal to

\sqrt{2} N

and

F_{2} is equal to (\sqrt{2} + \frac{1}{\sqrt{2}}) N

\begin{array}{l} ∴ F_{1} + \frac{1}{\sqrt{2}} = \sqrt{2} \\ F_{1} = \sqrt{2} - \frac{1}{\sqrt{2}} = \frac{2 - 1}{\sqrt{2}} = \frac{1}{\sqrt{2}} = 0 .707 N \\ and F_{2} = \sqrt{2} + \frac{1}{\sqrt{2}} = \frac{2 + 1}{\sqrt{2}} N = \frac{3}{\sqrt{2}} N = 2 .121 N \end{array}