Question

Two forces one of 12 N and another of 24 N act on a body in such a way that they make an angle of 90digry with each other find the resultant of the two forces

Answer 1

Force A=12N
Force B=24N
Resultant R=√(A^2+B^2+2ABcos theta)
=√(144+576+2*24*12*cos90°)
=√(144+576+576*0)
=√(720)
=26.833 N(approx.)

Answer 2

Given:

$F_1$ = 12N

$F_2$ = 24N

$\alpha$ = 90°

To find:

the resultant force of the two forces

Solution:

We know that when two forces $F_1$ and $F_2$ are applied on the same body and makes an angle $\alpha$ between each other, then the resultant force, $F_r$, acting on the body becomes

$F_r=\sqrt{F_1^2+F_2^2+2F_1F_2cos\alpha }$

Here,

$F_1$ = 12N

$F_2$ = 24N

$\alpha$ = 90°

Now, putting the values, according to the given statement,

$F_r=\sqrt{(12)^2+(24)^2+2(12)(24)(cos 90)}$

We know that, cos 90°=0,

=$\sqrt{144+576+0}$

$=\sqrt{720}$

=26.83N

Hence, the resultant force on the body is 26.83N.