When two equal forces are inclined at an angle 2 α, their resultant is twice as great as when they act at an angle 2 β, then

Question

When two equal forces are inclined at an angle 2 α, their resultant is twice as great as when they act at an angle 2 β, then (A)  cos α =2 cos β  (B)  cos α =2 sin β  (C)  cos β =2 cos α  (D)  sin β = cos α

Tardigrade Admin · Accepted Answer

Let the magnitude of each force be P. Then, R1= Resultant of two equal forces each of magnitude P inclined at an angle 2 α=2 P cos α, and R2= Resultant of two equal forces each of magnitude P inclined at an angle 2 β=2 P cos β It is given that, R1=2 R2 ⇒ 2 P cos α=4 P cos β ⇒ cos α=2 cos β

Q. When two equal forces are inclined at an angle $2 α$ , their resultant is twice as great as when they act at an angle $2 β$ , then

$cos α = 2 cos β$

$cos α = 2 sin β$

$cos β = 2 cos α$

$sin β = cos α$

Q. When two equal forces are inclined at an angle 2α, their resultant is twice as great as when they act at an angle 2β, then

cosα=2cosβ

cosα=2sinβ

cosβ=2cosα

sinβ=cosα

Let the magnitude of each force be P. Then, R1​= Resultant of two equal forces each of magnitude P inclined at an angle 2α=2Pcosα, and R2​= Resultant of two equal forces each of magnitude P inclined at an angle 2β=2Pcosβ It is given that, R1​=2R2​ ⇒2Pcosα=4Pcosβ ⇒cosα=2cosβ

Q. When two equal forces are inclined at an angle $2 α$ , their resultant is twice as great as when they act at an angle $2 β$ , then

$cos α = 2 cos β$

$cos α = 2 sin β$

$cos β = 2 cos α$

$sin β = cos α$