(a) Can a body with negative energy have momentum ?
(b) Two bodies having identical masses of 2 kg are moving towards each ther with same speed of 3 m/s along frictionless horizontal surface . The bodies stick together and come to rest . calculate the work done by external and internal forces on combined system of these two bodies .
(c ) Can a body have energy without momentum ?

Explanation

(a) Yes , it is possible in the case when K.E `lt` P.E .For example the electron in an atom has momentum but its total energy is negative .
(b) As there is no external force acting on the system of two bodies .
` :. " " F_(ext) = 0 `
`rArr W_("external") = vec(F)_("external") . vec (s ) = 0 `
By work energy theorem
Work done = change in K.E of the system =
Final K.E - Inital K.E
`W_("ext") +W_(int) = 0 - (1/2 mv^(2) +1/2 mv^(2)) = - mv^(2)`
`0 + W_("internal") = - mv^(2)`
`W_("internal ") = - mv^(2) = (-2) (3)^(2) = - 18 J `
(c ) Yes , a body can have energy without momentum
As K.E = `(P^(2))/(2m)`
If P = 0 , then K.E = 0
But total energy = K.E + P.E
= 0 +P.E (P.E may not or may not be zero )
Hence , a body can have energy without momentum .