If the total mechanical energy of a particle is zero, is its linear momentum necessarily zero? Is it necessarily non-zero ?

if total mechanical energy is 0 then is not necessary that monemtam is also 0...

if KE of particle is 10J & potential energy is -10J then total mechanical energy is 0

but due to KE its momentam exists ....

P = (2mKE)^1/2  

its not necessary that momentam is 0 when Mechanical energy is 0...

if particle is placed at surface of earth & we take surface as refrence  then total

mechanical energy is 0 ...no momentam exists ...

so momentam can be 0 or non zero if its mechanical energy is 0...

No it is not necessary that if mechanical energy is zero than momentum will be zero or non-zero.

Proof-

If PE = -(KE).

Than TE= PE + KE = 0.

But KE is not zero.

Also p(momentum) = 2KE/m.

So momentum is bot zero but M.E. is zero.