Question

Two unlike parallel forces $2\,N$ and $16\,N$ act at the ends of a uniform rod of length $21\,cm$. The point where the resultant acts is at a distance of ____ from the greater force.

• A. $4\,cm$
• B. $3\,cm$
• C. $2\,cm$
• D. $1\,cm$

Hint:

For unlike parallel forces, the resultant always lies outside the two forces and closer to the larger force.

Answer 1

The Correct Option is B

Concept: For two unlike parallel forces, the resultant lies outside the two forces on the side of the greater force. Using the principle of moments: \[ F_1d_1=F_2d_2 \]

Step 1: Write the given forces. \[ F_1=2N \] \[ F_2=16N \] Distance between them: \[ 21\,cm \] Let the resultant be at distance \(x\) from the larger force.

Step 2: Apply moment balance. \[ 16x=2(21+x) \] \[ 16x=42+2x \] \[ 14x=42 \] \[ x=3\,cm \]

Step 3: State the result. Hence the resultant acts outside the rod at a distance of \(3\,cm\) from the larger force. center minipage0.4

Distance from greater force = $3\,cm$ minipage center