An object flying in air with velocity $(20\hat{\mathrm{i}} + 25\hat{\mathrm{j}} - 12\hat{\mathrm{k}})$ suddenly breaks in two pieces whose masses are in the ratio 1: 5. The smaller mass flies off with a velocity $(100\hat{\mathrm{i}} + 35\hat{\mathrm{j}} + 8\hat{\mathrm{k}})$. The velocity of the larger piece will be

detailed solution

Correct option is A

Let m be the mass of an object flying with velocity v in air. When it gets split into two pieces of masses in ratio 1 : 5, the mass of smaller piece is m/6 and of bigger piece is 5m6.This situation can be interpreted diagrammatically as below.As, the object breaks in two pieces, so the momentum of the system will remains conserved, i.e. the total momentum (before breaking) = total momentum (after breaking)                     mv=m6v1+5m6v2⇒v=v16+5v26Given,  v= 20i^ + 25j^ - 12k^and      v1 = 100i^ + 35j^ + 8k^Putting these values in Eq. (i), we get(20i^+25j^-12k^)=(100i^+35j^+8k^)6+5v26⇒         (120i^+150j^-72k^)=(100i^+35j^+8k^)+5v2⇒          v2=15(20i^+115j^-80k^)                   =4i^ + 23j^ - 16k^