Question

Statement-1 : Two soild sphere of radius `r` and `2r`, made of same material, are kept in contact. The mutual grvitational force to attraction between them is proportional to `1//r^(4)`.
Statement-2 : Gravitational attraction between two point mass bodies varies inversely as the square of the distance between them.
A. Statement -1 is true , Statement -2 is true , Statement-2 is a correct explanation of Statement -1.
B. Statement -1 is true , Statement-2 is true , Statement-2 is a correct explanation of Statement-1.
C. Statement-1 is true , Statement-2 is false.
D. Statement-1 is false , Statement-2 is true.

Answer 1

Correct Answer - D
Here, statement-1 is wrong but statement-2 is correct. Let `rho` be the density of the material of each sphere.
Then, `M_(1) = (4)/(3) pi r^(3) rho`
and `M_(2) = (4)/(3) pi (2r^(3)) rho`
Disatnce between their centres `= r + 2r = 3r`
Now `F = (GM_(1)M_(2))/((3r)^(2))`
`= ((G(4pi)/(3) r^(3) rho)((4)/(3) pi 8 r^(3) rho))/(9r^(2))`
This gives `F prop r^(4)`