Question

Two lead balls each of mass m and 5m having radius r and 2r are separated by 12r.If they attract each other by gravitational force the distance covered by small sphere before they touch each other is

Answer 1

hence, distance covered by small ball before they touch each other is 7.5r .

let distance covered by small ball just before collision is x.

then, acceleration of smaller ball, a1 = 5GM/(12r - x)²

acceleration of bigger ball, a2 = GM/(12r - x)²

let after time t, balls collide to each other.

now, distance covered by smaller ball in time t, x1 = 1/2 a1t²

distance covered by bigger ball in time t , x2 = 1/2 a2t²

here, x1/x2 = a1/a2 = 5/1

or, x1 = 5x2 ......(1)

now, seperation between balls = 12r - (r + 2r)

or, x1 + x2 = 12r - 3r = 9r

or, x1 + x1/5 = 9r

or, 6x1 = 45r

or, 2x1 = 15r

or, x1 = 7.5r

hence, distance covered by small ball before they touch each other is 7.5r

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