Question

Given below are two statements: 
Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface 
Statement II : Acceleration due to earth's gravity is same at a height '\(h\)' and depth ' \(d\) ' from earth's surface, if \(h = d\).
In the light of above statements, Choose the most appropriate answer form the options given below

• A. Statement I is correct but statement II is incorrect
• B. Both Statement I and Statement II are incorrect
• C. Both Statement I and II are correct
• D. Statement I is incorrect but statement II is correct

Answer 1

The Correct Option is A

To determine the correct answer, we need to evaluate both statements based on the principles of gravitational physics.

1. Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
   • When you move away from the Earth's surface, either upwards (into space) or downwards (into the Earth), the gravitational acceleration decreases.
   • This can be understood using the formula for gravitational acceleration \( g \), which is derived from Newton's law of universal gravitation:
   • Here, \(G\) is the gravitational constant, \(M\) is the mass of the Earth, and \(r\) is the distance from the center of the Earth.
   • As you go up, \(r\) increases, causing \(g\) to decrease.
   • As you go down, effectively the shell of the Earth above you does not contribute to gravitational attraction, leading again to a decrease in \(g\) inside a uniform sphere.
   • Therefore, Statement I is correct.
2. Statement II: Acceleration due to earth's gravity is same at a height '\(h\)' and depth '\(d\)' from earth's surface, if \(h = d\).
   • This statement suggests that the gravitational acceleration at height \(h\) above the surface is the same as at depth \(d\) below the surface when \(h = d\).
   • When you go to height \(h\), the effective gravitational acceleration is given by:
   • Where \(g_0\) is the gravitational acceleration on the Earth's surface and \(R\) is the Earth's radius.
   • When you go to depth \(d\), the gravitational acceleration is:
   • Hence, for \(h = d\), \(g_h \neq g_d\). They are not equal as the effective gravitational field is reduced differently at height and depth.
   • Therefore, Statement II is incorrect.

In conclusion, the correct answer is "Statement I is correct but statement II is incorrect".