A block of mass `m` starts from rest and slides down a frictionless semi-circular track from a height h as shown. When it reaches the lowest point of the track, it collides with a stationary piece of putty also having mass m. If the block and the putty . stick together and continue to slide, the maximum height that the block-putty system could reach is

Options

A. `h/4`
B. `h/2`
C. `h`
D. independent of `h`

Answer

A

Explanation

`v_(0)=sqrt(2gh)` before collision
Applying conservation principe of mometum,
`mv_(0)=(m+m)u`
`:. u=v_(0)/2`
Applying conservation principle of momentum,
`1/2(2m)u^(2)=2mgh'`
`:. h'=u^(2)/(2g)impliesh'=v_(0)^(2)/(8g)`
`h'=(2gh)/(8g)impliesh'=h/4