JEE Advanced Model Paper 9 with solutions for online practice

The plate is free to rotate about vertical axis yy ' .

Let υ , υCM and ω be the velocity of the particle , velocity of centre of mass of plate andangular velocity of plate just after collision.
∴ From conservation of angular momentum about vertical axis passing through O is
mu

a

2

= mυ

a

2

+

ma2

3

ω ..... (i)
Since, the collision is elastic, the equation of coefficient of restitution is
e =

υCM−υ

u

= 1 ...... (ii)
But , υCM =

aω

2

...... (iii)
Solving equations (i) , (ii) and (iii) we get , ω =

12

7

u

a