Geostationary And Polar Satellites

A geostationary satellite completes one revolution in 24 hours. So its angular speed is: Here, Thus,
Hence, the correct answer is the option corresponding to:

Step 1: Understanding the Concept:
A geostationary satellite is one that appears stationary relative to a fixed point on the Earth's equator. For this to happen, the satellite must orbit the Earth in the same direction and with the exact same rotational period as the Earth's rotation on its own axis.
Step 2: Key Formula or Approach:
The relationship between angular velocity ( ) and time period ( ) is:

We need to use the known time period of a geostationary satellite and calculate .
Step 3: Detailed Explanation:
Since a geostationary satellite matches Earth's rotation, its orbital time period ( ) is exactly 1 day.
Time period, hours.
The question asks for angular velocity in units of radians per hour (rad hr ). Therefore, we keep the time period in hours.
Calculate angular velocity:


Simplify the fraction:

Step 4: Final Answer:
The angular velocity is rad hr .

Step 1: Use the formula for electric field.
The electric field intensity at the surface of a sphere is given by the formula: where is Coulomb's constant, is the charge, and is the radius of the sphere. Since the spheres are connected by a conducting wire, they must have the same potential, which implies that the ratio of the charges on the spheres will be proportional to the ratio of their radii.
Step 2: Relationship between charge and radius.
Let the charges on the two spheres be and , and their radii be and , respectively. Since the potential is the same, we have: This implies:
Step 3: Find the ratio of electric field intensities.
The electric field intensities at the surfaces of the spheres are: Substitute and : Now, calculate the ratio of electric field intensities:
Step 4: Conclusion.
The ratio of the electric field intensities at the surface of the two spheres is: