question_answer

A body weights \[500N\] on the surface of the earth. How much would it weigh half way below the surface of the earth?

A) \[1000N\]                           

B) \[500N\]

C) \[250N\]             

D)        \[125N\]

Correct Answer: C

Solution :

Value of acceleration due to gravity decreases on going below the surface of the earth. weight\[(w)\]of a body is defined as product of mass \[(m)\]and acceleration due to gravity\[(g)\]                                 \[w=mg\] The value of\[g\]below the surface of earth at a distance\[h\]is given by                 \[g=g\left( 1-\frac{h}{R} \right)\] \[\Rightarrow \]               \[W=w\left( 1-\frac{h}{R} \right)\] Given,\[h=\frac{R}{2},\,\,W=500\,\,N\]         \[W=500\left( 1-\frac{1}{2} \right)\]              \[=\frac{500}{2}=250\,\,N\]