Question

A ball on a string travels once around a circle with a circumference of 2. 0 m. The tension in the string is 5. 0 n.

Answer 1

The work done by the ball on a string is 0J if a ball is travelling around as circle with a circumference of 2.0m

We know that circumference or perimeter of circle=2πr where r is the radius of the circle.

So, we have circumference=2m

Therefore,2πr=2

=>r=2/2π

=>r=(1/π) m

Now, we know very well that when a body moves a displacement dx under the action of force, some amount of work is done by the force on the body and that force is given by

W=$\int\limits {F}. \, dx$

where F is defined as the force acting on the body

and dx is the displacement of the body.

On expanding the above formula, we get

=>W=Fdxcosθ where cosθ is the angle between the force and displacement of the body.

Since Tension is actually centripetal force which is acting along the center of the circle where ball displacement is in perpendicular direction to the tension.

It means angle between Tension and ball's displacement is 90°. So,cos90°=0

Therefore, W=Fdxcos90

=>W=0J.

Hence, amount of work done is 0J.

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(Complete question) is:

A ball on a string travels once around a circle with a circumference of 2. 0 m. The tension in the string is 5. 0 N. What amount of work done by the ball on the string?