Question

When a body is thrown upwards,its momentum first decreases and then increases.Is conservation of linear momentum violated here??

Answer 1

No Law of conservation of linear momentum is always true. Notice that in given situation there is an EXTERNAL FORCE on body due to earth's gravitation. Hence you can not apply Law of conservation of linear momentum here as it is valid only when there is no external force acting on the system.You have taken an isolated body not a system (for which this law is applicable).
Note: if the body and the earth are taken to be a system then then the force of gravitation is considered internal to the system . Hence linear momentum of System (body+earth) is conserved!

Answer 2

F = dP/dt where P is linear momentum and F is external force.

Now, if F = 0 then dP/dt = 0 which leads to the result that dP = 0, on integrating both sides we get, P = constant which means it is conserved.

But when there is external force applying on body, then its momentum can't be constant anymore.

Here in this case of throwing ball upwards, the ball is in action of many external forces like weight, air drag, etc which leads to change the momentum of the ball with time.

Hence, law of conversation of momentum is holds only when no external force acting on the body.