Questions
A tunnel is dug along a diameter of the earth. Find the force on a particle of mass M placed in the tunnel at a distance x from the center.
a
GMmR3
b
GMmxR2
c
GMmxR3
d
GMmx2R3
detailed solution
Correct option is C
Mass of earthM=Vρ=(4/3)πR3ρMass of imaginary sphere of radius x is M' ⇒ M=(4/3)πx3ρ (or) M∝R3⇒M'M=R'3R3⇒M'M=x3R3⇒M'=Mx3R3---(1) g'=GM'x2=GMx3R3x2 from (1) g'=GMxR3---(2) ⇒F=mg'=mGMxR3from equation(2)Talk to our academic expert!
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