Given data
*The momentum of the given body (A) is
[tex]p_A=10\text{ kg.m/s}[/tex]*The momentum of the given body (B) is
[tex]p_B=\frac{10\operatorname{kg}.m}{s}_{}[/tex]The formula for the momentum of the body (C) acquires immediately after the explosion is given as
[tex]p_C=\sqrt[]{p^2_A+p^2_B}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} p_C=\sqrt[]{(10)^2+(10)^2} \\ =\sqrt[]{200} \\ =10\sqrt[]{2}\text{ kg.m/s} \end{gathered}[/tex]Hence, the correct option is (c)
