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Two forces $P$ and $Q$ act at a point and have resultant $R$. If $Q$ is replaced by $2(R-P)$ acting in the direction opposite to that of $Q$, the resultant

1. remains same
2. becomes half
3. becomes twice
4. none of these

Correct answer: remains same

Solution

Since the original resultant is $R=P+Q$, we have $R-P=Q$. So the replaced force is $2(R-P)$ in the opposite direction of $Q$, which is equivalent to $2Q$ opposite to $Q$, i.e. $-2Q$. The new resultant is $P-2Q$, and using the given relation this simplifies to the same resultant as before.

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