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An object flying in air with velocity (20iˆ + 25jˆ − 12kˆ)
suddenly breaks in two pieces whose masses are in the ratio 1: 5. The smaller mass flies off with a velocity (100iˆ + 35jˆ + 8kˆ)
. The velocity of the larger piece will be?
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An object flying in air with velocity (20iˆ + 25jˆ − 12kˆ) suddenly br...
Initial Momentum Calculation
To find the velocity of the larger piece after the break, we start by calculating the initial momentum of the object. The initial velocity (V_initial) is given as:
- V_initial = (20i + 25j - 12k)
Assuming the mass of the smaller piece is 'm', the larger piece will then have a mass of '5m' (since their masses are in the ratio 1:5).
Final Momentum Calculation
Using the principle of conservation of momentum:
- Total initial momentum = Total final momentum
The total initial momentum (P_initial) is:
- P_initial = (20i + 25j - 12k) * (m + 5m) = (20i + 25j - 12k) * 6m
The smaller mass (m) flies off with a new velocity (V_smaller):
- V_smaller = (100i + 35j + 8k)
Thus, the final momentum of the smaller piece (P_smaller) will be:
- P_smaller = m * V_smaller = m * (100i + 35j + 8k)
Finding the Larger Piece's Velocity
Let the velocity of the larger piece be (V_larger). The final momentum of the larger piece (P_larger) will be:
- P_larger = 5m * V_larger
Applying conservation of momentum:
- (20i + 25j - 12k) * 6m = m * (100i + 35j + 8k) + 5m * V_larger
Dividing through by m:
- (20i + 25j - 12k) * 6 = (100i + 35j + 8k) + 5 * V_larger
Now we can express the equation to isolate V_larger:
Final Calculation of Velocity
Rearranging gives:
- 5 * V_larger = (20i + 25j - 12k) * 6 - (100i + 35j + 8k)
To find V_larger, divide the result by 5. Thus, the larger piece's final velocity can be calculated.
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An object flying in air with velocity (20iˆ + 25jˆ − 12kˆ) suddenly breaks in two pieces whose masses are in the ratio 1: 5. The smaller mass flies off with a velocity (100iˆ + 35jˆ + 8kˆ). The velocity of the larger piece will be?
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An object flying in air with velocity (20iˆ + 25jˆ − 12kˆ) suddenly breaks in two pieces whose masses are in the ratio 1: 5. The smaller mass flies off with a velocity (100iˆ + 35jˆ + 8kˆ). The velocity of the larger piece will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An object flying in air with velocity (20iˆ + 25jˆ − 12kˆ) suddenly breaks in two pieces whose masses are in the ratio 1: 5. The smaller mass flies off with a velocity (100iˆ + 35jˆ + 8kˆ). The velocity of the larger piece will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object flying in air with velocity (20iˆ + 25jˆ − 12kˆ) suddenly breaks in two pieces whose masses are in the ratio 1: 5. The smaller mass flies off with a velocity (100iˆ + 35jˆ + 8kˆ). The velocity of the larger piece will be?.
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