shakaib9876
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A bird sits on a uniform rod suspended from vertical wires P and Q.Image The rod has a weight W and is 15.0 cm long.The weight of the bird is 2W and acts at a distance x from P









What is the value of x when the tension in P is half the tension in Q?
A)7.50cm B)10.0cm C)11.3cm D)15.cm , The answer is C but I cant get to it
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Stonebridge
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How have you tried to get to it?
Did you take moments about the ends of the rod?
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Sophhhowa
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Take moments about both ends
Solve simultaneously
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Eimmanuel
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(Original post by shakaib9876)
A bird sits on a uniform rod suspended from vertical wires P and Q.Image The rod has a weight W and is 15.0 cm long.The weight of the bird is 2W and acts at a distance x from P









What is the value of x when the tension in P is half the tension in Q?
A)7.50cm B)10.0cm C)11.3cm D)15.cm , The answer is C but I cant get to it

Hi,

Welcome to TSR.


Although this question can be solved by setting 2 equations based on the principle of moments about both ends, I would still highly recommend the following (it is more simple IMO, yes it still involve 2 equations)

The resultant force is zero:

total upward forces = total downward forces

This allows finding the tension in P and Q in terms of W.
Spoiler:
Show
TP + TQ = Weight of rod + Weight of birdsT + 2T = W + 2W


Apply the principle of moment about P to solve for x.
Spoiler:
Show


Sum of clockwise moment about P = Sum of anti-clockwise moment about P

Weight of birds × perpendicular distance from P + Weight of rod × half the length of rod = TQ × length of rod

2W × x + W × 7.5 = 2W × 15.0
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