question_answer

A body weighs 500 N on the surface of the earth. How much would it weigh half way      below the surface of the earth?                                                                                                                                                   [BHU PMT-2004]

A)  1000 N                                

B)  500 N

C)  250 N                                   

D)  125 N

Correct Answer: C

Solution :

                 Key Idea: Value of acceleration due to gravity decreases on going below the surface of the earth. Weight \[\left( w \right)\] of a body is defined as product of mass \[\left( m \right)\] and acceleration due to gravity \[\left( g \right)\]                                                 \[w=mg\] 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, \[h=\frac{R}{2},\,w=500\,N\] \[\therefore \]  \[w'=500\left( 1-\frac{1}{2} \right)\]                                                 \[=\frac{500}{2}=250\,N\] Note : Value of \[g\] also decreases ongoing above the surface of earth, as follows                                                 \[g'=g\left( 1-\frac{21}{R} \right)\]