Two small bodies of masses 10 kg and 20 kg are kept a distnce 1.0 m apart and released. Assuming that only mutual gravitational force are acting, find the speeds of the particles when the separation decreases to 0.5 m.

Answer

A, B, D

Explanation

`K_(i) + U_(i) = K_(f) + U_(f)`
`underset(10 kg)overset(2V)(rarr)` `underset(20 kg)overset(V)(larr)`
`:. 0 - (Gm_(1)m_(2))/(r_(i)) = (1)/(2) xx 10 (2 nu)^(2) + (1)/(2) xx 20 nu^(2)`
`-(Gm_(1)m_(2))/(r_(f))`
`:. nu= sqrt((Gm_(1)m_(2))/(39)((1)/(r_(f)) - (1)/(r_(f)))`
`= sqrt((6.67 xx 10^(-11)xx 10 xx 20)/(30)((1)/(0.5) - (1)/(1)))`
`= 2.1 xx 10^(-5) m//s`
and `2 nu = 4.2 xx 10^(-5) m//s`