Home
Class 12
PHYSICS
Assuming the earth tobe a sphere of unif...

Assuming the earth tobe a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250N on the surface?

A

195 N

B

240 N

C

125 N

D

210 N

Text Solution

Verified by Experts

The correct Answer is:
C

At a depth d below the surface of the earth,
`mg'=G(M'm)/(R-d)^(2)`
`M'=(4)/(3)pi(R-d)^(3)rho`
`implies g'=(Gm')/(R-d)^(2)`
`=4/3Gpi(R-d)rho`
If `d=-(R)/(2)` then
`g'=(4)/(3)Gpi rho=(2piRrho)/(3)`
On the surface of the earth
`g=(Gm)/(RV)=4/3 pi GRrho`
`therefore g'=(g)/(2)`
`therefore ` The body weighted 250 N on the surface of the earth would weight `1/2 xx 250` =125 N , half way down towards the centre of the earth.
Promotional Banner

Similar Questions

Explore conceptually related problems

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighd 250 N on the surface ?

Assuming earth to be a sphere of uniform mass density, how much would a body weigh half way down the centre of the earth, if it weighed 100 N on the surface ?

Assuming earth to be a sphere of uniform mass density, how much would a body weigh half way down the center of the center of the earth , if it weighed 100 N on the surface?

Assuming the earth to be a sphere of uniform density, the acceleration due to gravity

A body weighs 250N on the surface of the earth. How much will it weighs half way down to the centre of the earth?

A body weighs 200N on the surface of the earth. How much will it weigh half way down to the center of the earth ?

A body weight 500 N on the surface of the earth. How much would it weigh half way below the surface of the earth

Assuming the earth to be a sphere of radius 6370 km, how many square kilometres is area of the land, if three-fourth of the earth’s surface is covered by water?

Assuming the earth to be a sphere of radius 6370 km, how many square kilometres is area of the land, if three-fourth of the earths surface is covered by water?

(a) Assuming the earth to be a sphere of uniform density, calculate the value of acceleration due to gravity at a point (i) 1600 km above the earth, (ii) 1600 km below the earth, (b) Also find the rate of variation of acceleration due to gravity above and below the earth's surface. Radius of earth =6400 km, g 9.8 m//s^(2) .