Question

a plank of mass M is moving with a velocity V along a frictionless horizontal track and a body of mass M/2 moving with a velocity 2v collides with plank elastically. Final speed of Plank is​

Answer 1

Explanation:

Let v

1

be the final velocity of block A

and v

2

be the final velocity of block B

Given that collision is elastic

So, momentum will be conserved also kinetic energy will be conserved

Applying momentum conservation ,

mv+

2

m

×2v=mv

1

+

2

m

×v

2

⟹v

1

+

2

v

2

=2v

⟹v

2

=4v−2v

1

---------------------------------(1)

Applying kinetic energy conservation

2

1

mv

2

+

2

1

×

2

m

(2v)

2

=

2

1

mv

1

2

+

2

1

2

m

v

2

2

⟹v

2

+2v

2

=v

1

2

+

2

v

2

2

⟹v

1

2

+

2

v

2

2

=3v

2

from eq (1) putting value of v

2

we get

⟹v 1/2 + 2(4v−2v 1 ) 2

=3v /2

⟹2v 1/2

+16v 2 +4v 1/2 −16vv /1

=6v /2

⟹6v 1/2 −16vv 1

+10v 2

=0

⟹6v 1/2

−6vv 1

−10vv 1

+10v 2

=0

⟹6v 1 (v 1

−v)−10v(v 1 −v)=0

⟹v 1

= 3/5v

because v 1

cannot be equal to v

So, Speed of block A after collision is

3

5v

Hope it helps✌️❤️