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The resultant of forces P and Q is R . If Q is doubled then R is doubled. If the direction of Q is reversed, then R is again doubled. Then P ^2: Q ^2: R ^2 is

Options

  1. A2: 3: 1
  2. B3: 1: 1
  3. C2: 3: 2
  4. D1: 2: 3

Correct answer

C. 2: 3: 2

Step-by-step solution

R ^2= P ^2+ Q ^2+2 PQ 4 R ^2= P ^2+4 Q ^2+4 PQ 4 R ^2= P ^2+ Q ^2-2 PQ On (1)+(2), 5 R ^2=2 P ^2+2 Q ^2 On (3) 2+(2), 12 R ^2=3 P ^2+6 Q ^2 2 P ^2+2 Q ^2-5 R ^2=0 3 P ^2+6 Q ^2-12 R ^2=0 P ^2 -24+30 = Q ^2 24-15 = R ^2 12-6 P ^2 6 = Q ^2 9 = R ^2 6 or P ^2: Q ^2: R ^2=2: 3: 2

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