A) \[1:1\]
B) \[1:2\]
C) \[2:1\]
D) \[1:4\]
Correct Answer: A
Solution :
Key Idea: Acceleration due to gravity decreases both at altitude and depth. If g is the acceleration due to gravity at a point, at a height h above the surface of earth, and g be acceleration due to gravity on earths surface, then \[g=g\left( 1-\frac{2h}{R} \right)\] ?.. (i) If g be the acceleration due to gravity at a point at depth d, below the surface of earth, then \[g=g\left( 1-\frac{d}{R} \right)\] ?. (ii) But, \[d=2h\] (given) \[\therefore \] \[g=g\left( 1-\frac{2h}{R} \right)\] ?. (iii) \[\therefore \] \[\frac{g}{g}=\frac{g\,\left( 1-\frac{2h}{R} \right)}{\left( 1-\frac{2h}{R} \right)}=1\] \[\therefore \] \[g\,:g=1:1\] Note: The value of acceleration due to gravity, also decreases due to rotation of earth.
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