The orbital speed of a satellite revolving around a planet in a circular orbit is `v_(0)` . If its speed is increased by 10 % ,then

Options

A. It will escape from its orbit
B. It will start rotating in an elliptical
C. It will continue to move in the same orbit
D. It will move in a circular orbit of radius 20 % more than radius of intial orbit

Answer

To solve the problem, we need to analyze the effects of increasing the orbital speed of a satellite by 10%.

### Step-by-Step Solution:

1. **Understanding Orbital Speed**:
The orbital speed \( v_0 \) of a satellite in a circular orbit is given by the formula:
\[ v_0 = \sqrt{\frac{GM}{r}} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the planet, and \( r \) is the radius of the orbit.

2. **Increasing the Speed**:
If the speed is increased by 10%, the new speed \( v \) can be expressed as:
\[ v = v_0 + 0.1v_0 = 1.1v_0 \]

3. **Centripetal Force and Gravitational Force**:
For a satellite in orbit, the centripetal force required to keep it in circular motion is provided by the gravitational force. The centripetal force \( F_c \) is given by:
\[ F_c = \frac{mv^2}{r} \]
The gravitational force \( F_g \) acting on the satellite is:
\[ F_g = \frac{GMm}{r^2} \]

4. **Setting Up the Equation**:
Initially, at speed \( v_0 \):
\[ \frac{mv_0^2}{r} = \frac{GMm}{r^2} \]
This shows that the centripetal force equals the gravitational force.

5. **Substituting the New Speed**:
Now, substituting \( v = 1.1v_0 \) into the centripetal force equation:
\[ F_c' = \frac{m(1.1v_0)^2}{r} = \frac{m(1.21v_0^2)}{r} \]

6. **Comparing Forces**:
The new centripetal force becomes:
\[ F_c' = 1.21 \cdot \frac{mv_0^2}{r} \]
Since we know that \( \frac{mv_0^2}{r} = \frac{GMm}{r^2} \), we can substitute:
\[ F_c' = 1.21 \cdot \frac{GMm}{r^2} \]
This indicates that the new centripetal force \( F_c' \) is greater than the gravitational force \( F_g \).

7. **Conclusion**:
Since the centripetal force \( F_c' \) exceeds the gravitational force \( F_g \), the satellite will no longer be able to maintain its orbit and will escape. Therefore, the correct conclusion is that the satellite escapes from its orbit.

### Final Answer:
The satellite escapes from its orbit.