An object initially at rest explodes into 3 fragments A, B and C. The momentum of A is $P \hat{i}$ and that of B is $\sqrt{3}P\hat{j}$ where P is a positive number. The momentum of C will be:

Question

( A ) 2 P in a direction making $150^{\circ}$ with that of A
( B ) $(1+\sqrt{3})$ P in a direction making $120^{\circ}$ with that of A
( C ) 2 P in a direction making $150^{\circ}$ with that of B
( D ) $(1+\sqrt{3})$ P in a direction making $150^{\circ}$ with that of B