Question

Two identical sphetes are placed in contact with rach other.The force of gravitation between two spheres will be propotional to (R=radius of each sphere)
options are:
a)R square
b)R power -2
c)R power 4
d)R power -4
answer it full with explanation

Answer 1

Since, Gravitational force = F = $\frac{G \times m \times M}{D2}$

where m, M are masses of two bodies

"D" is distance between them.

As it is given that, sphere are identical

So, F = $\frac{G \times m \times M}{{2R}^{2}}$

we know that, mass = density × volume ; i.e.,m = pv ,

= $\frac{G {(p \times V)}^{2}}{{4R}^{2}}$

= ($\frac{{(Gp)}^{2}}{{4R}^{2}}$) [( $\frac{4}{3}$)πR³]² (sphere volume = (4/3)πR³)

F = (4/3)π²p²R⁴

F ∝ R⁴

Thus , Answer is "C) R power 4"