Question

Two forces P ans Q acting at a point have a resultant R. If P is doubled , R is doubled and P is reversed in direction, even then R is doubled . Show that P:Q:R=√(6):√(2):√(5).​

Answer 1

Answer:

Step-by-step explanation:

Two forces P ans Q acting at a point have a resultant R. If P is doubled , R is doubled and P is reversed in direction, even then R is doubled . Show that P:Q:R=√(6):√(2):√(5).​

R² = P² + Q² + 2PQCosθ  - eq 1

P doubled , R doubled

(2R)² = (2P)² + Q² + 2(2P)QCosθ

4R² = 4P² + Q² + 4PQCosθ  b - eq 2

P is reversed , R is doubled

4R² = P² + Q² - 2PQCosθ   - eq3

Eq 3 - Eq 1

3R² = -4PQCosθ  

Putting in Eq 2

7R² = 4P² + Q²     - Eq 4

Eq 3 + Eq1

5R² = 2P² + 2Q²    - Eq 5

2 * Eq4 - Eq5

9R² = 6P²

3R² = 2P²

2*Eq5 - Eq 4 -

3R² = 3Q²

2P² = 3Q² = 3R²

=> P² : Q² : R²  = 1/2  :  1/3  : 1/3

=> P² : Q² : R²  = 6  :  4  : 4

=> P : Q : R = √6 :  2 :  2

Answer 2

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