When two forces of magnitude P and Q are perpendicular to each other, their resultant is of magnitude R. When they are at an angle of `180^(@)` to each other, their resultant is of magnitude `(R )/(sqrt2)`. Find the ratio of P and Q.

Options

A. `sqrt3 +- 2`
B. `2 +- sqrt3`
C. `3 +- sqrt5`
D. `5 +- sqrt3`

Answer

B

Explanation

`P^(2) + Q^(2) = R^(2)` ….(i)
`|P - Q| = (R )/(sqrt2)` ….(ii)
Squaring (2). `P^(2) + Q^(2) - 2PQ = (R^(2))/(2)` …..(iii)
from (1) & (3)
`2PQ = (R^(2))/(2)`
`P^(2) + Q^(2) = R^(2) = 4PQ`
`P^(2) - 4PQ + Q^(2) = 0`
`(P^(2))/(Q^(2)) - (4P)/(Q) + 1 = 0`
`(P)/(Q) = (4 +- 2 sqrt3)/(2) = 2 +- sqrt3`