Question

The resultant of ⃗⃗ ⃗⃗ ⃗⃗ . If ⃗⃗ is

doubled, ⃗⃗ is doubled; when Q is reversed, ⃗⃗

is again doubled. Find P: Q: R.​

Answer 1

Answer:

resultant of the same magnitude F. The ... P and Q are in the ratio 3:1. Which of ... N. If they act at right angles to each other, ... doubled, � �⃗⃗ is doubled; when Q is reversed,

so ratio =4:2:1

Answer 2

Answer:

√2:√3:√2

Explanation:

According to the given problem,

(i) The resultant of two forces P and Q is R.

(ii) If Q is doubled, R is doubled.

(iii) If Q is reversed, R is again doubled.

(iv) What is the ratio of P^2 : Q^2 : R^2?

From (i) we get following relation,

R^2 = P^2 + Q^2 + 2*P*Q*cosθ …… (1a) [θ is the angle between vectors P & Q ]

From (ii) we get following relation,

4*R^2 = P^2 + 4*Q^2 + 4*P*Q*cosθ …… (1b)

From (iii) we get following relation,

4*R^2 = P^2 + Q^2 - 2*P*Q*cosθ …… (1c)

From (1a) + (1c) we get,

5*R^2 = 2*P^2 + 2*Q^2 …… (1d)

From (1b) + 2*(1c) we get,

12*R^2 = 3*P^2 + 6*Q^2

or 4*R^2 = P^2 + 2*Q^2 …… (1e)

From (1d) - (1e) we get,

R^2 = P^2 …… (1f)

From 2*(1e) - (1d) we get,

3*R^2 = 2*Q^2 …… (1g)

Therefore from (1f) & (1g) we get,

3*P^2 = 2*Q^2 = 3*R^2

or P^2/2 = Q^2/3= R^2/2 [dividing all by the L.C.M. (= 6)]

or P^2 : Q^2 : R^2 = 2 : 3 : 2 [Ans]