At what depth below the surface of the Earth does the acceleration due to gravity become zero?
A. At a depth equal to one-fourth the radius of the Earth
B. At a depth equal to half the radius of the Earth
C. It never becomes zero
D. At the center of the Earth
Answer: Option D
Solution (By JKSSB Mock Tests)
The acceleration due to gravity at a depth 'd' is given by g' = g(1 - d/R), where R is the radius of the Earth. If we go to the center of the Earth, the depth 'd' becomes exactly equal to R. Substituting d = R into the formula gives g' = g(1 - R/R) = g(1 - 1) = 0. So, gravity is zero at the core.
According to Kepler's Third Law of Planetary Motion, the square of the time period of revolution of a planet around the Sun is directly proportional to:
A.The cube of the semi-major axis of its elliptical orbit
B.The square of the semi-major axis of its elliptical orbit
Explanation:
Kepler's Third Law (Law of Periods) states that the square of the time period (T^2) of any planet is proportional to the cube of the semi-major axis (r^3) of its orbit. Mathematically, T^2 is proportional to r^3. This law helps in calculating orbital periods or distances of planets and satellites.
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