An object flying in air with velocity (20î+ 25 $\hat{j}$ - 12 $\hat{k}$ ) m s⁻¹ suddenly breaks into two pieces whose masses are in the ratio 1 : 5. The smaller piece moves with velocity (100 $\hat{i}$ + 35 $\hat{j}$ + 8 $\hat{k}$ ) m s⁻¹. Find the velocity of the larger piece.
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Question

An object flying in air with velocity (20î+ 25 $\hat{j}$ - 12 $\hat{k}$ ) m s⁻¹ suddenly breaks into two pieces whose masses are in the ratio 1 : 5. The smaller piece moves with velocity (100 $\hat{i}$ + 35 $\hat{j}$ + 8 $\hat{k}$ ) m s⁻¹. Find the velocity of the larger piece.

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G1 Physics · Accepted Answer

Step 1: Let the fragment masses be m and 5m; the original mass is 6m. Step 2: During the short breakup interval, linear momentum is conserved: 6m v₀ = m v₁ + 5m v₂, so 5v₂ = 6v₀ - v₁. Step 3: Insert v₀ = 20i + 25j - 12k and v₁ = 100i + 35j + 8k. Then 5v₂ = (120-100)i + (150-35)j + (-72-8)k = 20i + 115j - 80k. Step 4: v₂ = 4i + 23j - 16k m s⁻¹. Correct answer: A. The uploaded book misprints the smaller fragment's velocity; values here are checked against the NEET 2019 original.