Quantum Mechanics

To solve this problem, we need to understand the relationship between the time period of a satellite's orbit and its orbital radius. Kepler's Third Law of Planetary Motion states that the square of the period of revolution of a satellite is directly proportional to the cube of the semi-major axis of its orbit (which is the radius in the case of a circular orbit):

Thus, for a satellite in orbit, the relationship can be written as:

where is a constant of proportionality that depends on the gravitational constant and the mass of the Earth.

Let's denote the time period of the first satellite as and its orbital radius as . Thus,

For the second satellite with orbital radius , its time period is given by:

Taking the ratio of the two time periods squared:

Simplifying this equation gives:

Calculating :

Thus,

Taking the square root on both sides gives:

This implies that is approximately 1.045 times the period of the first satellite, or 4.5% larger.

So, the time period of revolution of the second satellite is approximately larger than the first one by 4.5%. Hence, the correct answer is:

4.5%

Concept:
Extension of a wire under load is given by where = applied force, = length of wire, = cross-sectional area, = Young's modulus.
Step 1: Find extension of first string. Force applied: Thus, Step 2: Find extension of second string. Force applied: Length , Young's modulus . Step 3: Find the ratio.

Step 1: Equation for whole system Let acceleration of wedge be . For horizontal motion of system: Using

Step 2: Acceleration of block relative to wedge Along the incline: Step 3: Solve equations Substitute (2) into (1): Solving, Step 4: Time taken Relative displacement: