Show that the period of a body of mass m revolving in a horizontal circle with constant velocity of the end of a string of length L is independent mass of the object?

The period of a body revolving in a horizontal circle is the time it takes for the body to complete one full revolution. The period can be calculated using the formula:

T = 2πr/v

Where:
T = period
r = radius of the circle
v = velocity of the body

In the case of a body revolving in a horizontal circle with a string of length L, the radius of the circle is equal to the length of the string, so r = L.

Given that the velocity of the body is constant, it means that the centripetal force acting on the body is also constant. The centripetal force required to keep the body moving in a circle is given by:

F = mv^2/r

Substituting r = L into the equation, we get:

F = mv^2/L

Since the centripetal force is constant, it means that the period of the body is also constant, regardless of the mass of the body. Therefore, the period of a body revolving in a horizontal circle with a constant velocity at the end of a string of length L is independent of the mass of the object.

The time period of a body of mass m attached to the end of a string of length L revolving in a horizontal circle with constant velocity is given by:
$$T=2\pi\sqrt{\frac{L}{g}}$$
Where:
- T is the time period
- L is the length of the string
- g is the acceleration due to gravity.

From the above equation, it is clear that the time period T is independent of the mass of the object m. This means that the mass of the object does not affect the time period of its revolution in a horizontal circle.