# 12.12.1. Resultant of Parallel Coplanar Forces

A uniform rod having a length of m and weighing N is resting in a horizontal position on two supports, where the support is at the end , and is at a distance from the end . Find the reaction of the support and the distance , given that .

• AN, cm
• BN, cm
• CN, cm
• DN, cm

### Example

A uniform rod having a length of m and weighing N is resting in a horizontal position on two supports, where the support is at the end , and is at a distance from the end . Find the reaction of the support and the distance , given that .

### Solution

The total reaction acting on the rod is equal to the weight. Using the relation of the reaction forces given in the question, we get

The moment of a force about a point is the product of the magnitude of the force and the perpendicular distance between the force and that point.

Taking moments around :

Since the rod is in equilibrium, the sum of algebraic measures of moments is equal to zero.

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