Question

The range of a projectile of weight \( W \) is \( R \). The average torque on the projectile between the initial and final positions \( P \) and \( Q \) about the point of projection is:

• A. \( \frac{WR}{2} \)
• B. \( \frac{WR}{3} \)
• C. \( \frac{WR}{4} \)
• D. \( WR \)

Hint:

The average torque is half the product of the weight and range of the projectile.

Answer 1

The Correct Option is A

The torque on the projectile is defined as the moment of the force at a given point. The average torque between two points \( P \) and \( Q \) on the projectile's path is given by: \[ \text{Average Torque} = \frac{1}{2} \times \text{Force} \times \text{Distance} \] Here, the force on the projectile is its weight \( W \) and the distance between \( P \) and \( Q \) is the range \( R \). Therefore, the average torque is: \[ \text{Average Torque} = \frac{WR}{2} \] Thus, the average torque between the initial and final positions \( P \) and \( Q \) is \( \frac{WR}{2} \).