Question

Two particles of masses my and my separated by a distance d are at rest initially. If they
move towards each other under mutual interaction (say electric, gravitational or elastic).
where will they meet?

a. At the centre of line joining the two particles
b. Anywhere in between two masses
c. At the centre of mass of the system of two particles
d. None of the above​

Answer 1

Answer:

By applying law of conservation of momentum,

m

1

v

1

−m

2

v

2

=0⇒m

1

v

1

=m

2

v

2

........ (i)

Where v

1

and v

2

are the velocities of masses m

1

and m

2

at a distance r from each other.

By conservation of energy,

Change in P.E= change in K.E.

r

Gm

1

m

2

=

2

1

m

1

v

1

2

+

2

1

m

2

v

2

2

........ (ii)

Solving eqn. (i) and (ii) we get

v

1

=

r(m

1

+m

2

)

2Gm

2

2

and v

2

=

r(m

1

+m

2

)

2Gm

1

2

Relative velocity of approach, v

R

=∣v

1

∣+∣v

2

∣=

r

2G

(m

1

+m

2

)

Option is B