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Question: P and Q are like parallel forces. If P is moved parallel to itself through a distance x, then the re...

P and Q are like parallel forces. If P is moved parallel to itself through a distance x, then the resultant of P and Q moves through a distance.

A

PxP+Q\frac{Px}{P + Q}

B

PxP−Q\frac{Px}{P - Q}

C

PxP+2Q\frac{Px}{P + 2Q}

D

None

Answer

PxP+Q\frac{Px}{P + Q}

Explanation

Solution

Let the parallel forces P and Q act at A and B respectively. Suppose the resultant P + Q acts at C.

Then, AC=(ABP+Q)QAC = \left( \frac{AB}{P + Q} \right)Q .....(i)

If P is moved parallel to itself through a distance x i.e. at A'.

Suppose the resultant now acts at C'. Then ,

A′C′=(A′BP+Q)QA'C' = \left( \frac{A'B}{P + Q} \right)Q ⇒ A′C′=(AB−xP+Q)QA'C' = \left( \frac{AB - x}{P + Q} \right)Q .....(ii)

Now CC′=AC′−AC=AA′+A′C′−ACCC' = AC' - AC = AA' + A'C' - AC

⇒CC′=x+(AB−xP+Q)Q−(ABP+Q)Q⇒CC′=x−QxP+Q⇒CC′=PxP+Q\Rightarrow CC' = x + \left( \frac{AB - x}{P + Q} \right)Q - \left( \frac{AB}{P + Q} \right)Q \Rightarrow CC' = x - \frac{Qx}{P + Q} \Rightarrow CC' = \frac{Px}{P + Q}