Rohini satellite is at a height of 500 km. and Insat-B is at a height of 3600 km. from surface of earth then relation between their orbital velocity `(V_R,V_I)` is :

Options

A. `V_RgtV_1`
B. `V_RltV_1`
C. `V_R=V_1`
D. No relation

Explanation

To find the relation between the orbital velocities of the Rohini satellite and INSAT-B, we can follow these steps:

### Step 1: Understand the formula for orbital velocity
The orbital velocity \( V \) of a satellite is given by the formula:

\[ V = \sqrt{\frac{GM}{r}} \]

where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth,
- \( r \) is the distance from the center of the Earth to the satellite.

### Step 2: Define the heights and distances
Given:
- Height of Rohini satellite \( h_R = 500 \) km,
- Height of INSAT-B satellite \( h_I = 3600 \) km.

The radius of the Earth \( R \) is approximately \( 6400 \) km. Therefore, the distances from the center of the Earth to the satellites are:
- For Rohini satellite:
\[ r_R = R + h_R = 6400 \text{ km} + 500 \text{ km} = 6900 \text{ km} \]
- For INSAT-B satellite:
\[ r_I = R + h_I = 6400 \text{ km} + 3600 \text{ km} = 10000 \text{ km} \]

### Step 3: Write the expressions for orbital velocities
Using the formula for orbital velocity, we can write:
- For Rohini satellite:
\[ V_R = \sqrt{\frac{GM}{r_R}} = \sqrt{\frac{GM}{6900 \text{ km}}} \]
- For INSAT-B satellite:
\[ V_I = \sqrt{\frac{GM}{r_I}} = \sqrt{\frac{GM}{10000 \text{ km}}} \]

### Step 4: Find the ratio of the orbital velocities
Now, we can find the ratio of the orbital velocities:
\[ \frac{V_R}{V_I} = \frac{\sqrt{\frac{GM}{6900}}}{\sqrt{\frac{GM}{10000}}} \]
This simplifies to:
\[ \frac{V_R}{V_I} = \sqrt{\frac{10000}{6900}} \]

### Step 5: Simplify the ratio
Calculating the square root:
\[ \frac{V_R}{V_I} = \sqrt{\frac{10000}{6900}} \approx \sqrt{1.449} \approx 1.207 \]

### Conclusion
Since \( V_R > V_I \), we conclude that the orbital velocity of the Rohini satellite is greater than that of the INSAT-B satellite.

### Final Relation
Thus, the relation between their orbital velocities is:
\[ V_R > V_I \]