Question:
A fighter plane is moving in a vertical circle of radius \( r \). Its minimum velocity at the highest point \( A \) of the circle will be:
A fighter plane is moving in a vertical circle of radius \( r \). Its minimum velocity at the highest point \( A \) of the circle will be:
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At the highest point of a vertical circle, the minimum velocity is determined by balancing the gravitational force and the centripetal force. The correct velocity ensures the plane just stays in the circle.
Updated On: Apr 22, 2026
- \( \sqrt{3gr} \)
- \( \sqrt{2gr} \)
- \( \sqrt{gr} \)
- \( \sqrt{gr/2} \)
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The Correct Option is C
Solution and Explanation
Step 1: Apply the concept of minimum velocity.
At the highest point of the vertical circle, the velocity should be such that the plane just completes the circular motion. The tension in the string is zero at this point. The only force acting on the plane is the gravitational force, and it provides the necessary centripetal force.
Step 2: Centripetal force at the highest point.
The centripetal force required to keep the plane in motion at the highest point is: \[ F_c = \frac{m v^2}{r} \] where \( m \) is the mass of the plane, \( v \) is the velocity, and \( r \) is the radius of the circle.
Step 3: Gravitational force.
The gravitational force \( mg \) acts downward and provides the required centripetal force. Thus, at the highest point, we have: \[ mg = \frac{m v^2}{r} \] Simplifying: \[ v^2 = gr \] Taking the square root: \[ v = \sqrt{gr} \] Thus, the minimum velocity at the highest point is \( \sqrt{gr} \).
At the highest point of the vertical circle, the velocity should be such that the plane just completes the circular motion. The tension in the string is zero at this point. The only force acting on the plane is the gravitational force, and it provides the necessary centripetal force.
Step 2: Centripetal force at the highest point.
The centripetal force required to keep the plane in motion at the highest point is: \[ F_c = \frac{m v^2}{r} \] where \( m \) is the mass of the plane, \( v \) is the velocity, and \( r \) is the radius of the circle.
Step 3: Gravitational force.
The gravitational force \( mg \) acts downward and provides the required centripetal force. Thus, at the highest point, we have: \[ mg = \frac{m v^2}{r} \] Simplifying: \[ v^2 = gr \] Taking the square root: \[ v = \sqrt{gr} \] Thus, the minimum velocity at the highest point is \( \sqrt{gr} \).
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