Question

Two equal forces of magnitude p each are angled first at 60 deg later at 120deg. The ratio of magnitude of their resultant is?
(1) 1:ur3
(2)ur3:1
(3)1:1
(4)1:2

Answer 1

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Answer 2

Answer:

The ratio of the magnitude of their resultant is $\frac{\sqrt{3}}{1}$ i.e.option(2).

Explanation:

Force is a vector quantity.

Suppose a vector is represented as

$\vec r=a\hat{i}+b\hat{k}$             (1)

And the resultant of this vector will be,

$r=\sqrt{A^2+B^2+2ABcos\theta}$      (2)

Where θ is the angle between the vectors.

As per the question the forces are of equal magnitude i.e."p"

And,

θ₁=60°

θ₂=120°

So, by using equation (2) we get;

$r_1=\sqrt{q^2+q^2+2q^2cos 60\textdegree}=\sqrt{2q^2+2q^2\times \frac{1}{2}}=\sqrt{3q^2}=\sqrt{3}q$     (3)

$r_2=\sqrt{q^2+q^2+2q^2cos 120\textdegree}=\sqrt{2q^2+2q^2\times \frac{-1}{2}}=\sqrt{2q^2-q^2}=\sqrt{q^2}=q$  (4)

Now as required in question,

$\frac{r_1}{r_2}=\frac{\sqrt{3}q}{q}=\frac{\sqrt{3}}{1}$                (5)

Hence, the ratio of the magnitude of their resultant is $\frac{\sqrt{3}}{1}$ i.e.option(2).