If `upsilon_e` denotes escape velocity and `V_0` denotes orbital velocity of a satellite revolving around a planet of radius R, then

Options

A. `upsilon_e=sqrt2.upsilon_o`
B. `upsilon_e=2upsilon_o`
C. `2upsilon_e=upsilon_o`
D. `sqrt2.upsilon_e=upsilon_o`

Explanation

To find the relationship between escape velocity (\(v_e\)) and orbital velocity (\(V_0\)) of a satellite revolving around a planet of radius \(R\), we can start by using the formulas for both velocities.

### Step 1: Write the formula for orbital velocity
The orbital velocity (\(V_0\)) of a satellite in a circular orbit is given by the formula:
\[ V_0 = \sqrt{\frac{GM}{R}} \]
where \(G\) is the gravitational constant and \(M\) is the mass of the planet.

### Step 2: Write the formula for escape velocity
The escape velocity (\(v_e\)) from the surface of a planet is given by the formula:
\[ v_e = \sqrt{\frac{2GM}{R}} \]

### Step 3: Relate escape velocity to orbital velocity
Now, we can express the escape velocity in terms of the orbital velocity. We notice that:
\[ v_e = \sqrt{2} \cdot \sqrt{\frac{GM}{R}} = \sqrt{2} \cdot V_0 \]

### Step 4: Final relationship
Thus, we can conclude that:
\[ v_e = \sqrt{2} \cdot V_0 \]

This means that the escape velocity is \(\sqrt{2}\) times the orbital velocity.

### Conclusion
The relationship between escape velocity and orbital velocity is:
\[ v_e = \sqrt{2} \cdot V_0 \]