AP EAMCET Engineering 20 Apr 2019 Shift 2 Paper

The expression of the mass of the earth is
Me=ρV
Me=ρ(‌

4

3

πR3)
The gravitational force on the body of mass m due to earth is,

F=‌

GMem

(R+h)2

F=‌

Gρ( 4 3 πR3)m

(R+h)2

F=‌

4

3

πGRρm(1+‌

h

R

)−2

or ,F=‌

4

3

πGRρm(1−‌

2h

R

)
Thus the difference in weight is,

F=‌

4

3

πGRρm−‌

4

3

πGρmR(‌

2h

R

)

F=‌

4

3

πGRρm−‌

8

3

πρGmh

The error in weight is
‌ Error ‌=‌

8

3

πρGmh