Spheres A and B of uniform density have masses 1 kg and 100 kg respectively. Their centres are separated by 100m.(ii) Find the gravitational force on An due to the earth. [M_("(earth)")=6xx10^(24)kg, R_("(earth)")=6400km]

Spheres A and B of uniform density have masses 1 kg and 100 kg respect

1.	Spheres A and B of uniform density have masses 1 kg and 100 kg respectively. Their centres are separated by 100m.(ii) Find the gravitational force on An due to the earth. [M_("(earth)")=6xx10^(24)kg, R_("(earth)")=6400km]
Answer» Solution :Data : `m_(1)=1kg, m_(2)kg, r = 100m`, `M=6xx10^(24)kg, R = 6400km=6400xx10^(3)m,` `t=1s, s=1cm=1xx10^(-2)m,` `G=6.67xx10^(-11)N.m^(2)//kg^(2)` `F_(1)=?, F_(2)=?, v_(1)=? , t_(1)=?, v_(2)=? , t_(2)=?` (III) Ignoring VARIATION of acceleration with distance, `v_(1)=u_(1)+at=0+(F_(1))/(m_(1))t=(6.67xx10^(-13)N)/(1kg)xx1s` `=6.67xx10^(-13)m//s` This velocity is directed from A to B. As the separation between A and B decreases, the acceleration of A and hence the velocity of A will increase. Ignoring variation of acceleration with distance, `s_(1)=ut+(1)/(2)at^(2)=0+(1)/(2)(F_(1))/(m_(1))t_(1)^(2)` `therefore t_(1)^(2)=(2m_(1)s_(1))/(F_(1))` `therefore t_(1)^(2)=(2xx1kgxx10^(-2)m)/(6.67xx10^(-18)N)=3xx10^(10)s^(2)` `therefore t_(1)=1.732xx10^(5)s`