Question

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

Answer 1

Acceleration due to gravity is given as,

g = GM/R^2

If radius of earth contracted by 0.1%, then new radius will be

R' = 0.999R

g' = GM/R'^2 = GM/(0.999R)^2

g' = g/0.9992 = 1.002g

So new weight will be

W' = 1.0002W

Now increase in weight will be

[(W'-W)/W] x 100 = (1.002W-W/W) x 100 = (1.002-1) x 100

Percentage increase in weight = 0.2%

Answer 2

Answer:

Explanation:

Acceleration due to gravity is given as,

g = GM/R^2

If radius of earth contracted by 0.1%, then new radius will be

R' = 0.999R

g' = GM/R'^2 = GM/(0.999R)^2

g' = g/0.9992 = 1.002g

So new weight will be

W' = 1.0002W

Now increase in weight will be

[(W'-W)/W] x 100 = (1.002W-W/W) x 100 = (1.002-1) x 100

Percentage increase in weight = 0.2%