Question

Given below are two statements:
Statement I : Acceleration due to gravity is different at different places on the surface of earth
Statement II : Acceleration due to gravity increases as we go down below the earth's surface
In the light of the above statements, choose the correct answer from the options given below

• A. Both Statement I and Statement II are false
• B. Statement $I$ is false but Statement II is true
• C. Statement I is true but Statement II is false
• D. Both Statement I and Statement II are true

Answer 1

The Correct Option is C

$g_{\text{eff}}=g-{\omega }^2{R}_e{\sin }^2\theta ,\theta \to$ co-latitude angle
$g_{\text{eff}}=g\left(1-\frac{d}{R_e}\right),d$ here depth

Answer 2

Acceleration due to gravity is given by: \[ g_{\text{eff}} = g - \omega^2 R \sin^2\theta \] which depends on latitude. Inside the Earth, gravity decreases with depth as: \[ g_{\text{eff}} = g \left( 1 - \frac{d}{R} \right), \quad d \text{ is depth.} \] Thus, Statement I is true but Statement II is false.