Question

Ques no. 5
5. Two particle of masses 4 kg, 8 kg, are separated by a distance of 12m. If they are moving towards each other under the influence of a mutual force of attraction, then the two particles will meet, each other at a distance of from 8 kg mass.
(a) 6 m (b) 2 m (c) 4 m (d) 8 m

Answer 1

First, we have to find the attraction force by using the gravitational force theorem.

force (F) = GMm/r²

Where, G = Newtonian constant of gravitation

       M,m = value of masses

          r = distance between two masses

Then we can use an equation of linear motion to find the distance.

        S = ut + (1/2)at²

Where, S = traveled distance

            U = initial velocity

             t = time to travel s distance

            a= acceleration

But we know that initial velocities of 4kg and 8kg are zero. Then we can modify above equation as below,

           S = (1/2)at²

By using Newton's second law, (a= F/m)

           S = (1/2) * (F/m)* t²

Force (F) and time(t) are constants for both two masses.

Therefore,   distance is inversely proportional to the mass of the object

           S ∝ 1/m

for 8 kg

          a ∝ 1/8------- (1)

for 4 kg

         12-a ∝ 1/4------- (2)

dividing equation (1) by (2),

      $a/(12-a) = 4/8$

       $2a = 12-a$

       $3a = 12$

distance traveled by 8 kg is = a = 4 m