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A block initially at rest breaks into two parts of masses in the ratio 2: 3. The velocity of smaller part is (81+6j) m/s. Find the velocity of bigger part.?
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A block initially at rest breaks into two parts of masses in the ratio...
Introduction
When a block breaks into two parts, the principle of conservation of momentum applies. The total momentum before the split must equal the total momentum after the split.
Given Data
- Mass ratio of smaller part (m1) to bigger part (m2): 2:3
- Velocity of smaller part (v1): (81 + 6j) m/s
Mass Calculation
Let the masses of the smaller and larger parts be:
- m1 = 2x
- m2 = 3x
The total mass (M) of the block before breaking is M = m1 + m2 = 2x + 3x = 5x.
Since the block is initially at rest, its initial momentum is zero.
Momentum Conservation
According to the conservation of momentum:
Initial Momentum = Final Momentum
0 = (m1 * v1) + (m2 * v2)
Substituting the known values:
0 = (2x * (81 + 6j)) + (3x * v2)
Simplifying the Equation
Dividing through by x (assuming x is not zero):
0 = 2 * (81 + 6j) + 3 * v2
Now, rearranging to find v2:
3 * v2 = -2 * (81 + 6j)
Calculating v2
v2 = (-2/3) * (81 + 6j)
Calculating the components:
- Real part: (-2/3) * 81 = -54
- Imaginary part: (-2/3) * 6 = -4
Thus, the velocity of the bigger part (v2) is:
Final Result
v2 = (-54 - 4j) m/s
This means the bigger part moves in the opposite direction with a velocity of 54 m/s in the real component and 4 m/s in the imaginary component.
When a block breaks into two parts, the principle of conservation of momentum applies. The total momentum before the split must equal the total momentum after the split.
Given Data
- Mass ratio of smaller part (m1) to bigger part (m2): 2:3
- Velocity of smaller part (v1): (81 + 6j) m/s
Mass Calculation
Let the masses of the smaller and larger parts be:
- m1 = 2x
- m2 = 3x
The total mass (M) of the block before breaking is M = m1 + m2 = 2x + 3x = 5x.
Since the block is initially at rest, its initial momentum is zero.
Momentum Conservation
According to the conservation of momentum:
Initial Momentum = Final Momentum
0 = (m1 * v1) + (m2 * v2)
Substituting the known values:
0 = (2x * (81 + 6j)) + (3x * v2)
Simplifying the Equation
Dividing through by x (assuming x is not zero):
0 = 2 * (81 + 6j) + 3 * v2
Now, rearranging to find v2:
3 * v2 = -2 * (81 + 6j)
Calculating v2
v2 = (-2/3) * (81 + 6j)
Calculating the components:
- Real part: (-2/3) * 81 = -54
- Imaginary part: (-2/3) * 6 = -4
Thus, the velocity of the bigger part (v2) is:
Final Result
v2 = (-54 - 4j) m/s
This means the bigger part moves in the opposite direction with a velocity of 54 m/s in the real component and 4 m/s in the imaginary component.
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A block initially at rest breaks into two parts of masses in the ratio 2: 3. The velocity of smaller part is (81+6j) m/s. Find the velocity of bigger part.?
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A block initially at rest breaks into two parts of masses in the ratio 2: 3. The velocity of smaller part is (81+6j) m/s. Find the velocity of bigger part.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A block initially at rest breaks into two parts of masses in the ratio 2: 3. The velocity of smaller part is (81+6j) m/s. Find the velocity of bigger part.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A block initially at rest breaks into two parts of masses in the ratio 2: 3. The velocity of smaller part is (81+6j) m/s. Find the velocity of bigger part.?.
A block initially at rest breaks into two parts of masses in the ratio 2: 3. The velocity of smaller part is (81+6j) m/s. Find the velocity of bigger part.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A block initially at rest breaks into two parts of masses in the ratio 2: 3. The velocity of smaller part is (81+6j) m/s. Find the velocity of bigger part.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A block initially at rest breaks into two parts of masses in the ratio 2: 3. The velocity of smaller part is (81+6j) m/s. Find the velocity of bigger part.?.
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