Question

A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle \(\theta\) with the horizontal. The weight experienced by the person is:

• A. \(\frac{W}{2}\)
• B. W
• C. \(W cos\theta\)
• D. \(W sin\theta\)

Answer 1

The Correct Option is A

This scenario analyzes the weight distribution when a heavy iron bar is supported at its ends: one on the ground and the other on a person's shoulder. The solution proceeds as follows:

Problem Description:

• A static, balanced iron bar forms an angle \(\theta\) with the horizontal, supported by the ground and a person's shoulder.
• This is a typical physics problem concerning equilibrium and force distribution.

Governing Principle:

• For a uniformly balanced rod at two support points, the weight is equally divided between these points when the rod is symmetrically positioned.
• Consequently, the total weight \(W\) is shared equally between the ground and the shoulder.

Methodology:

1. Treat the iron bar as a uniform rod with its center of mass (and thus gravitational force) at its midpoint.
2. Due to symmetry and equilibrium, the forces exerted by the ground and the shoulder must collectively balance the bar's weight.
3. Each support point thus bears half of the bar's total weight.
4. Therefore, the force exerted on the person's shoulder is \(\frac{W}{2}\).

Conclusion:

• The weight supported by the person is \(\frac{W}{2}\), as the bar's weight is distributed equally between the two support points.

The weight experienced by the person is: \(\frac{W}{2}\).