question_answer

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

A)  \[Q(P+Q)X\]

B)  \[\frac{QX}{(P+Q)}\]

C)  \[\frac{PX}{(P+Q)}\]

D)  \[\frac{(P+Q)X}{(P-Q)}\]

Correct Answer: B

Solution :

Let the parallel forces P and Q act at A and B respectively. Suppose the resultant \[(P+Q)\] acts at C. Then,   \[BC=\left( \frac{AB}{P+Q} \right)p\] ?.(i) If Q is moved parallel to itself through a distance x ie, at B? suppose the resultant now acts at C?. Then, \[B'C'=\left( \frac{AB'}{P+Q} \right)P\] \[\Rightarrow \] \[B'C'=\left( \frac{AB+x}{P+Q} \right)P\] ?.(ii) Now, \[CC'=CB'-B'C'\] \[=BC+BB'-B'C'\] \[=\left( \frac{AB}{P+Q} \right)P+x-\left( \frac{AB+x}{P+Q} \right)P\] \[=\frac{-xP}{P+Q}+x\] \[=\frac{xQ}{P+Q}\]