First slide

Vectors

Question

Two forces 3 N and 2 N are at an angle $θ$ such that the resultant is R. The first force is now increased to 6 N and the resultant become 2R. The value of $θ$ is

Moderate

A

$30^{0}$
B

$60^{0}$
C

$90^{0}$
D

$120^{0}$

Solution

A = 3 N, B = 2 N then R = $\sqrt{A^{2} + B^{2} + 2 ABcosθ}$
R = $\sqrt{9 + 4 + 12 cosθ}$
Now A = 6 N, B = 2 N then
2R = $36 + 4 + 24 cosθ$
from (i) and (ii) we get $cosθ = - \frac{1}{2}$
$∴ θ {= 120}^{0}$

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