Question

the resultant of two forces is perpendicular to one of them if the forces are 500 gram wait, 250 gram weight find the angle between two forces

Answer 1

Answer:

$\theta=\frac{2\pi}{3}$

Explanation:

We are given that

$\midF_1\mid=500 gram weight$

$\midF_2\mid=250 g wt$

We know that Resultant =R=$F_1+F_2$

We are given that Resultant is perpendicular to one force

We have to find the angle between two forces

$R\cdot F_2=0$ (because resultant is perpendicular to one force )

$(F_1+F_2)\cdotF_2=0$

$F_1.F_2+\mid F_2\mid^2=0$

$\mid F_1\mid\mid F_2\mid\cos\theta+(250)^2 g^2=0$

$500\cdot250 g^2cos\theta=-62500 g^2$

$cos\theta=\frac{62500}{500\cdot250}$

$\costheta=-\frac{1}{2}$

$cos\theta=-cos\frac{\pi}{3}$

$\theta$lies in second quadrant therefore

$cos\theta=cos(\pi-\frac{\pi}{3})$

$cos\theta=cos\frac{2\pi}{3}$

$\theta=\frac{2\pi}{3}$

Hence, the angle between two forces=$\frac{2\pi}{3}$

Answer 2

answer is 120°

I hope this helps uou