if radius of earth contracted by 0.1%, its mass remaining same, then weight of the body at earth's surface will increase by

a 0.1%

b 0.2%

c 0.3%

d Remains same

with reason

the acceleration due to gravity is given as

g = GM/R²

now if the radius if decreased by 0.1%, the new radius will be

R' = 0.999R

so, the new acceleration due to gravity will be

g' = GM/R'² = GM / (0.999R)²

or

g' = g / 0.9992 = 1.002g

so, the new weight will be given as

W' = 1.0002W

niw, the increase in weight will be

[(W' - W) / W] x 100 = (1.002W - W / W) x 100 

= (1.002 - 1) x 100

or

percentage increase in weight = 0.2 %

the correct answer is option (b).