A body of mass 2kg is moving in a vertical circle of radius 2m . The work done when it moves from the lowest point to the highest point is

The correct option is 80 J.

When a body moves in a vertical circle, it experiences the force of gravity acting vertically downwards. The work done by gravity or against gravity depends on the vertical displacement of the body.

Let us break down the solution step-by-step:

1. Identify the given values:
Mass of the body, _m = 2 kg
Radius of the vertical circle, _r = 2 m
Acceleration due to gravity, _g ≈ 10 m/s² (standard value used for calculation)

2. Determine the vertical displacement:
The body moves from the lowest point of the vertical circle to the highest point.
The lowest point is at the bottom of the circle, and the highest point is at the top of the circle.
Therefore, the vertical height _h ascended by the body is equal to the diameter of the circle.
$$h=2\cdot r$$ Substituting the value of radius:
$$h=2\cdot 2\text{ m}=4\text{ m}$$

3. Calculate the work done against gravity:
The work done in lifting a mass _m through a vertical height _h against gravity is given by the formula:
$$W=m\cdot g\cdot h$$ Substituting the known values:
$$W=2\text{ kg}\cdot 10\text{ m/s}{2}^{}\cdot 4\text{ m}$$ $$W=80\text{ J}$$

Thus, the work done in moving the body from the lowest point to the highest point is 80 J.