Spheres A and B of uniform density have masses 1 kg and 100 kg respectively. Their centers are separated by 100m. (iv.) If A begins to fall, starting from rest, due to the earth's downward pull, what will be its velocity after one second ? How much time will it take to fall through 1 cm ?
`[M_("(earth)")=6xx10^(24)kg, R_("(earth)")=6400km]`

Explanation

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)=?`

(iv) `v_(2)=u_(2)+at=0 +g t =(F_(2))/(m_(1))t`
`=(9.77N)/(1kg)xx1s=9.77m//s" (downward)"`
`[|v_(2)|gtgt|v_(1)|]`
`s_(2)=ut+(1)/(2)at^(2)=0+(1)/(2)g t_(2)^(2)=(1)/(2)(F_(2))/(m_(1))t_(2)^(2)`
`therefore" "t_(2)^(2)=(2s_(2)m_(1))/(F_(2))=(2xx10^(-2)mxx1kg)/(9.77N)=0.205s^(2)`
`therefore t_(2)=0.453s" "[t_(1)gt gt t_(2)]`