Question

Two forces, whose magnitude are at the ratio of 3 : 5 give a resultant of 35 N. If angle of inclination is 60°, find magnitude of each force(H.P.S.S.C.E. 2004)​

Answer 1

Answer:

15 N and 25 N respectively.

Explanation:

Given :

Magnitude two forces are in 3 : 5 .

Resultant is 35 N and angle is 60.

Let the constant ratio be k

So first two become 3 k and second 5 k.

We have resultant formula

$\displaystle R=\sqrt{P^2+Q^2+2 \ PQ \ \cos\theta}$

Put the values here we get

$\displaystle 35=\sqrt{(3k)^2+(5k)^2+2\times \ 3k \times5k \ \cos60}$

Squaring on both side

$\displaystle \text{ (35)^2=\left(\sqrt{(3k)^2+(5k)^2+2\times \ 3k \times5k \ \times\dfrac{1}{2}}\right)^2 }\\\\\displaystle 1225=\left((3k)^2+(5k)^2+3k \times5k\right)\\\\\displaystyle 1225=\left(9k^2+25k^2+15k^2\right)\\\\\displaystle 1225=(49k^2)\\\\\displaystle k^2=25\\\\\displaystle k=\pm5$

Thus magnitude of first force = 5 × 3 = 15 N

Magnitude of second force = 5 × 5 = 25 N

Thus we get answer.