Question

The resultant of two forces P and Q is R. If one of the forces is reversed in
direction, then the resultant becomes S. Then for the identity R² + S² = 2(P² + Q²) to
hold good
(a) The forces are collinear
(b) The forces act as right angles to each other
(c) The forces are inclined at 45° to each other
(d) The forces can have any angle of inclination between them

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Answer 1

Given info : The resultant of two forces P and Q is R. If one of the forces is reversed in  direction, then the resultant becomes S. Then for the identity R² + S² = 2(P² + Q²) to  hold good

To check :

• a) The forces are collinear
• (b) The forces act as right angles to each other
• (c) The forces are inclined at 45° to each other
• (d) The forces can have any angle of inclination between them

solution : case 1 : the resultant of two forces P and Q is R.

i.e., P + Q = R

⇒ P² + Q² + 2PQcosФ = R² , let Ф is angle between P and Q.

Case 2 : one of the forces is reversed in direction,

i.e., |P-Q|=|S|

⇒ P² + Q² - 2PQcosФ = S²

now, R² + S² = 2(P² + Q²) [ given ]

⇒ (P² + Q² + 2PQcosФ) + (P² + Q² - 2PQcosФ) = 2(P² + Q²)

we see that the identity is independent of angle between forces. so the force can have any angle of inclination between them.

therefore the correct option is (d) the force can have any angle of inclination between them.