Question

The resultant of two forces 3p and root3p is root 12p the angle between the two forces is​

Answer 1

Answer:

The angle will be 90 degrees

Answer 2

$\maltese$Given to find the angle between them :-

Resultant force of 3p, $\sqrt{3}p$ is $\sqrt{12}p$

$\maltese$Solution :-

We have formula for finding the resultant force that is

${\boxed{F_r = \sqrt{(F_1)^2+(F_2)^2+2F_1F_2cos\theta}}}$

$\maltese$Substituting these values in formula

$\sqrt{12}p=\sqrt{(3p)^2+\sqrt{(3p)^2} +2 \times 3p\times\sqrt{3}p \:cos\theta}$

$\maltese$Squaring on both sides

$(\sqrt{12}p)^2=\bigg(\sqrt{(3p)^2+\sqrt{(3p)^2} +2 \times 3p\times\sqrt{3} p \:cos\theta) }\bigg)^2$

$12p^2={(3p)^2+\sqrt{(3p)^2} +2 \times 3p\times\sqrt{3} pcos\theta}$

$12p^2=9p^2+3p^2+\sqrt{18p^2} cos\theta$

$12p^2 = 12p^2 +\sqrt{18} p cos\theta$

$\sqrt{18} p cos\theta = 12p^2-12p^2$

$\sqrt{18} p cos\theta = 0$

$cos\theta =\dfrac{0}{\sqrt{18}p }$

$cos\theta = 0$

$cos\theta = cos90^{\circ}$

So, $\theta = 90^{\circ}$

$\maltese$So, the angle between the two forces is 90°