The square of resultant of two equal forces is three times their product. Angle between the forces is

Question

The square of resultant of two equal forces is three times their product. Angle between the forces is (A)  π  (B)  (π /2)  (C)  (π /4)  (D)  (π /3)

Tardigrade Admin · Accepted Answer

Let θ be the angle between vectors vec P and vec Q whose resultant is vec R . Here, P=Q and R2=3 P Q=3 P2 As R2=P2+Q2+2 P Q cos θ ∴ 3 P2=P2+P2+2 P2 cos θ or 3 P2-2 P2=2 P2 cos θ or P2=2 P2 cos θ or 1=2 cos θ ∴ cos θ=(1/2), thus, cos θ= cos 60° or θ=60°=(π/3)

Q. The square of resultant of two equal forces is three times their product. Angle between the forces is

$π$

$\frac{π}{2}$

$\frac{π}{4}$

$\frac{π}{3}$

Q. The square of resultant of two equal forces is three times their product. Angle between the forces is

π

2π​

4π​

3π​

Let θ be the angle between vectors P and Q​ whose resultant is R. Here, P=Q and R2=3PQ=3P2 As R2=P2+Q2+2PQcosθ ∴3P2=P2+P2+2P2cosθ or 3P2−2P2=2P2cosθ or P2=2P2cosθ or 1=2cosθ ∴cosθ=21​, thus, cosθ=cos60∘ or θ=60∘=3π​

$π$

$\frac{π}{2}$

$\frac{π}{4}$

$\frac{π}{3}$