An object flying in air with velocity suddenly breaks into two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity The velocity of the larger piece will be: [2019]

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Q.
An object flying in air with velocity $(20 \hat{i} + 25 \hat{j} - 12 \hat{k})$ suddenly breaks into two pieces whose masses are in the ratio 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: [2019]

1 $4 \hat{i} + 23 \hat{j} - 16 \hat{k}$

2 $- 100 \hat{i} - 35 \hat{j} - 8 \hat{k}$

3 $20 \hat{i} + 15 \hat{j} - 80 \hat{k}$

4 $- 20 \hat{i} - 15 \hat{j} - 80 \hat{k}$

Ans.
(1)

From the law of conservation of linear momentum $m \vec{v} = m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}$

$\Rightarrow 6 k (20 \hat{i} + 25 \hat{j} - 12 \hat{k}) = k (100 \hat{i} + 35 \hat{j} + 8 \hat{k}) + 5 k {\vec{v}}_{2}$

$\Rightarrow 5 {\vec{v}}_{2} = (120 - 100) \hat{i} + (150 - 35) \hat{j} + (- 72 - 8) \hat{k}$

$\Rightarrow 5 {\vec{v}}_{2} = 20 \hat{i} + 115 \hat{j} - 80 \hat{k} \Rightarrow {\vec{v}}_{2} = 4 \hat{i} + 23 \hat{j} - 16 \hat{k}$

Solution

Q.
An object flying in air with velocity $(20 \hat{i} + 25 \hat{j} - 12 \hat{k})$ suddenly breaks into two pieces whose masses are in the ratio 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: [2019]

1 $4 \hat{i} + 23 \hat{j} - 16 \hat{k}$

2 $- 100 \hat{i} - 35 \hat{j} - 8 \hat{k}$

3 $20 \hat{i} + 15 \hat{j} - 80 \hat{k}$

4 $- 20 \hat{i} - 15 \hat{j} - 80 \hat{k}$

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Solution

Q. An object flying in air with velocity (20i^+25j^-12k^) suddenly breaks into two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity (100i^+35j^+8k^). The velocity of the larger piece will be: [2019]

1 4i^+23j^-16k^

2 -100i^-35j^-8k^

3 20i^+15j^-80k^

4 -20i^-15j^-80k^

Ans. (1) From the law of conservation of linear momentum mv→=m1v→1+m2v→2 ⇒6k(20i^+25j^-12k^)=k(100i^+35j^+8k^)+5kv→2 ⇒5v→2=(120-100)i^+(150-35)j^+(-72-8)k^ ⇒5v→2=20i^+115j^-80k^ ⇒ v→2=4i^+23j^-16k^

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Q.
An object flying in air with velocity $(20 \hat{i} + 25 \hat{j} - 12 \hat{k})$ suddenly breaks into two pieces whose masses are in the ratio 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: [2019]

1 $4 \hat{i} + 23 \hat{j} - 16 \hat{k}$

2 $- 100 \hat{i} - 35 \hat{j} - 8 \hat{k}$

3 $20 \hat{i} + 15 \hat{j} - 80 \hat{k}$

4 $- 20 \hat{i} - 15 \hat{j} - 80 \hat{k}$