If the resultant of two forces of magnitude p and 2 p is perpendicular to p, then the angle between the forces is

Question

If the resultant of two forces of magnitude p and 2 p is perpendicular to p, then the angle between the forces is (A) (2 π/3) (B) (3 π/4) (C) (4 π/5) (D) (5 π/6)

Tardigrade Admin · Accepted Answer

tan α=(2 p sin θ/p+2 p cos θ) here θ=90° ⇒ ∞=(2 p sin θ/p+2 p cos θ) ⇒ p+2 p cos θ=0 ⇒ cos θ=(1/2) ⇒ θ=(2 π/3)

Q. If the resultant of two forces of magnitude $p$ and $2 p$ is perpendicular to $p$ , then the angle between the forces is

$\frac{2 π}{3}$

$\frac{3 π}{4}$

$\frac{4 π}{5}$

$\frac{5 π}{6}$

$tan α = \frac{2 p s i n θ}{p + 2 p c o s θ}$ here $θ = 9 0^{\circ}$
$\Rightarrow \infty = \frac{2 p s i n θ}{p + 2 p c o s θ}$
$\Rightarrow p + 2 p cos θ = 0$
$\Rightarrow cos θ = \frac{1}{2}$
$\Rightarrow θ = \frac{2 π}{3}$

Q. If the resultant of two forces of magnitude p and 2p is perpendicular to p, then the angle between the forces is

32π​

43π​

54π​

65π​