To determine which statements are true for a body moving with constant speed on a circular track, let's analyze each statement one by one. ### Given Statements: 1. **I. Its velocity is constant** 2. **II. No work is done on the body** 3. **III. It has constant acceleration directed away from the centre** 4. **IV. The centripetal force is directed towards the centre** ### Analyzing Each Statement: #### Statement I: Its velocity is constant - **Explanation**: This statement is **false**. While the speed of the body is constant (meaning it covers equal distances in equal intervals of time), its velocity is not constant because velocity is a vector quantity that includes both speed and direction. In circular motion, the direction of the velocity vector is continuously changing as the body moves along the circular path. Therefore, the velocity is not constant. #### Statement II: No work is done on the body - **Explanation**: This statement is **true**. Work is defined as the product of force and the displacement in the direction of the force. In uniform circular motion, the centripetal force acts towards the center of the circle, while the displacement of the body is tangential to the circle. Since the angle between the centripetal force and the displacement is 90 degrees, the work done (W = F * d * cos(θ)) is zero because cos(90°) = 0. Thus, no work is done on the body. #### Statement III: It has constant acceleration directed away from the centre - **Explanation**: This statement is **false**. In uniform circular motion, the acceleration is not constant in direction away from the center; rather, it is centripetal acceleration, which is always directed towards the center of the circle. This acceleration is responsible for changing the direction of the velocity vector, keeping the body in circular motion. #### Statement IV: The centripetal force is directed towards the centre - **Explanation**: This statement is **true**. The centripetal force is indeed directed towards the center of the circular path. This force is necessary to keep the object moving in a circle and is responsible for the centripetal acceleration that acts on the body. ### Summary of True Statements: - The true statements are **II** (No work is done on the body) and **IV** (The centripetal force is directed towards the centre). ### Correct Option: - The correct option is **A. II and IV**. ### Why Other Options Are Incorrect: - **B. I and IV**: This option is incorrect because while IV is true, I is false (velocity is not constant). - **C. II and III**: This option is incorrect because II is true, but III is false (acceleration is directed towards the center, not away). - **D. I and III**: This option is incorrect because both I and III are false. ### Revision Summary: - In uniform circular motion, speed is constant, but velocity is not due to changing direction. - No work is done on the body because the centripetal force is perpendicular to the displacement. - Centripetal acceleration is directed towards the center of the circular path. - The correct combination of true statements regarding a body moving in a circular track is II and IV.