Question

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

• A. 4 cm
• B. 3 cm
• C. 2 cm
• D. 1 cm

Hint:

When two forces act along the same line, use the principle of moments to find the position of the resultant force.

Answer 1

The Correct Option is A

Let the force of 2 N be \( F_1 \) and the force of 16 N be \( F_2 \). The length of the rod is 21 cm. To find the point where the resultant acts, we use the formula for the position of the resultant force: \[ x = \frac{F_2 \times d_2}{F_1 + F_2} \] Where: - \( F_1 = 2 \, \text{N} \), \( F_2 = 16 \, \text{N} \) - \( d_2 = 21 \, \text{cm} \) Now, substituting the values: \[ x = \frac{16 \times 21}{2 + 16} = \frac{336}{18} = 18.67 \, \text{cm} \] The distance from the greater force (16 N) is \( 18.67 \, \text{cm} \). Thus, the correct answer is 4 cm.