Gravitation

JEE Main level, single correct, medium

59 of 223

Question 59 of 223

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth d=R2d=\dfrac{R}{2} from the surface of earth, if its weight on the surface of earth is 200N200N, will be : (Given R=R= radius of earth)

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Answer: (B) 100N100N

The acceleration due to gravity with depth is
g′=g(1−dR){g}^{'}=g\left(1-\dfrac{d}{R}\right)
The given data is
W=200Nd=R2W=200N d=\dfrac{R}{2}
Let the weight be at the given depth, W′W'. Hence, the value is
mg′=mg(1−R2R)=m(g2)m{g}^{'}=mg\left(1-\dfrac{\dfrac{R}{2}}{R}\right)=m\left(\dfrac{g}{2}\right)
The Weight W′W' =W2=2002=100N=\dfrac{W}{2}=\dfrac{200}{2}=100N

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