The kinetic energy needed to project a body of mass m from the earth's surface to infinity is

Explanation

To find the kinetic energy needed to project a body of mass \( m \) from the Earth's surface to infinity, we can use the principle of conservation of energy. Here’s a step-by-step solution:

### Step 1: Understand the energy at the surface and at infinity
At the Earth's surface, the body has both kinetic energy and gravitational potential energy. At infinity, the potential energy is zero, and we want to find the kinetic energy needed to ensure that the body reaches this point.

### Step 2: Write down the expressions for kinetic and potential energy
The kinetic energy (\( KE \)) of the body when projected is given by:
\[
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