Question

The greatest and least and resultant of two forces are $7N$ and $3N$ respectively . If each of the force is increased by $3N$ and applied ${60}^{\circ }.$ The magnitude of the resultant is

• A. $7N$
• B. $3N$
• C. $10N$
• D. $\sqrt{129}N$

Answer 1

The correct option is D $\sqrt{129}N$

Let , magnitude of the two forces be $F_1$ and $F_2$.

Given,

for gr ether resultant $\theta =0^0$

$\begin{array}{c}=\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos 0}\\ =\sqrt{{\left(F_1+F_2\right)}^2}\\ =F_1+F_2=7N............\left(i\right)\\ Now,forleastresul\tan t\theta ={180}^0\\ =\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos }180\\ =\sqrt{{\left(F_1+F_2\right)}^2\hat{A}}\\ =F_1+F_2=3N............\left(ii\right)\end{array}$

Adding equation (i) and (ii) we get,

$2F_1=10;F_1=5N$

Putting value of $F_1$ in (i) we get,

$F+2=2N$

After adding $3N$ to each force we get,

$F_1^{\prime }=8N$

$F_2^{\prime }=5N$

When they are applied at $\theta ={60}^0$

Resultant force $F$ will be,

After solving we will get,

$F=\sqrt{129}N$