An object flying in the air with velocity (20i + 25j - 12k) suddenly breaks into two pieces whose masses are in the ratio of 1 : 5 . The smaller mass - PHYSICS MCQ NEET 2019 2026 | ExamTest.live

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

Solution & Step-by-step Explanation

Let the total mass be 6 m . The pieces have masses m and 5 m .By conservation of momentum: P_{ini t ia l} = P_{f ina l} 6 m v = m v_{1} + 5 m v_{2} 6 (20 \hat{i} + 25 \hat{j} - 12 \hat{k}) = 1 (100 \hat{i} + 35 \hat{j} + 8 \hat{k}) + 5 v_{2} (120 \hat{i} + 150 \hat{j} - 72 \hat{k}) - (100 \hat{i} + 35 \hat{j} + 8 \hat{k}) = 5 v_{2} 20 \hat{i} + 115 \hat{j} - 80 \hat{k} = 5 v_{2} v_{2} = 4 \hat{i} + 23 \hat{j} - 16 \hat{k} .

Try it yourself before checking the explanation above.

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

4 \hat{i} + 23 \hat{j} - 16 \hat{k}

- 100 \hat{i} - 35 \hat{j} - 8 \hat{k}

20 \hat{i} + 15 \hat{j} - 80 \hat{k}

- 20 \hat{i} - 15 \hat{j} - 80 \hat{k}

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