Gravitation

JEE Main level, single correct, medium

61 of 223

Question 61 of 223

The weight of a body on the earth is 400N.400N. Then weight of the body when taken to a depth half of the radius of the earth will be:

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Answer: (A) 200N200N

The acceleration due to gravity changes with depth from the surface, which is given by
g′=g(1−dR)...(i)g'=g\left(1-\dfrac{d}{R}\right)...(i)
The given data is
W=400Nd=R2W=400N d=\dfrac{R}{2}
Multiplying equation (i) with the mass we get the weight.
mg′=mg(1−R2R)=mg(12)⇒W′=400N2=200Nmg'=mg\left(1-\dfrac{\dfrac{R}{2}}{R}\right)=mg\left(\dfrac{1}{2}\right) \Rightarrow W'=\dfrac{400N}{2}=200N

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