How intense is 80 dB sound in comparison to 40 dB?
(A) 10^4
(B) 10^2
(C) 2
(D) 1/2

Correct Answer: A. Infinity
Gravitational potential energy (UU) at a distance rr from the center of the Earth is given by:
U=−GMmrU = -\frac{GMm}{r}
Where:
• GG = Gravitational constant
• MM = Mass of the Earth
• mm = Mass of the object
• rr = Distance from the center of the Earth
Key Concepts:
1. Gravitational Potential Energy is Negative:
Since gravity is an attractive force, the potential energy is always negative, becoming less negative (closer to zero) as the object moves farther from the Earth.
2. At Different Locations:
o At the Earth's Surface (r=Rr = R):
U=−GMmRU = -\frac{GMm}{R}
This is a finite negative value, indicating the gravitational potential energy at the surface.
o At the Earth's Center (r=0r = 0):
The potential energy approaches an undefined state, as the formula is not valid inside the Earth. Practically, the potential energy would be very negative.
o At Twice the Earth's Radius (r=2Rr = 2R):
U=−GMm2RU = -\frac{GMm}{2R}
This is less negative than the potential energy at the surface, indicating higher energy.
o At Infinity (r→∞r \to \infty):
As rr increases without limit, the potential energy approaches zero, which is the maximum possible value since UU increases with rr.
Gravitational potential energy is maximum at infinity, where U=0U = 0, because this represents the point where the object is no longer under the influence of Earth's gravitational pull.
Thus, the correct answer is: A. Infinity.