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A circular lamina moves with its plane parallel to the x-y plane of a reference frame S at rest. Assuming its motion to be along the axis of x (or y), calculate the velocity at which surface area would appear to be reduced to half to an observer in frame S?
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A circular lamina moves with its plane parallel to the x-y plane of a ...
Problem Statement
A circular lamina moves with its plane parallel to the x-y plane of a reference frame S at rest. Assuming its motion to be along the axis of x (or y), calculate the velocity at which surface area would appear to be reduced to half to an observer in frame S?
Solution
Explanation of the problem
The problem describes the motion of a circular lamina (a thin, flat, circular object) in a reference frame S. The lamina is moving along the x-axis (or y-axis), while its plane is parallel to the x-y plane of the reference frame S. The problem asks to find the velocity at which the surface area of the lamina would appear to be reduced to half to an observer in frame S.
Formula to calculate surface area
The surface area of a circular lamina is given by the formula:
A = πr^2
Where A is the surface area, and r is the radius of the lamina.
Formula to calculate apparent area
The apparent area of the lamina as seen by the observer in frame S is given by the formula:
A' = A/γ
Where A' is the apparent area, A is the actual surface area, and γ is the Lorentz factor, which is given by:
γ = 1/√(1 - v^2/c^2)
Where v is the velocity of the lamina along the x-axis (or y-axis), and c is the speed of light.
Formula to calculate velocity
To find the velocity at which the surface area would appear to be reduced to half, we can set A' = A/2 and solve for v. This gives us the formula:
v = c/√(3)
Conclusion
The velocity at which surface area would appear to be reduced to half to an observer in frame S is given by the formula v = c/√(3), where c is the speed of light. This formula is derived using the Lorentz factor, which takes into account the relativistic effects of the motion of the lamina.
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A circular lamina moves with its plane parallel to the x-y plane of a reference frame S at rest. Assuming its motion to be along the axis of x (or y), calculate the velocity at which surface area would appear to be reduced to half to an observer in frame S?
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A circular lamina moves with its plane parallel to the x-y plane of a reference frame S at rest. Assuming its motion to be along the axis of x (or y), calculate the velocity at which surface area would appear to be reduced to half to an observer in frame S? for Teaching 2024 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about A circular lamina moves with its plane parallel to the x-y plane of a reference frame S at rest. Assuming its motion to be along the axis of x (or y), calculate the velocity at which surface area would appear to be reduced to half to an observer in frame S? covers all topics & solutions for Teaching 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular lamina moves with its plane parallel to the x-y plane of a reference frame S at rest. Assuming its motion to be along the axis of x (or y), calculate the velocity at which surface area would appear to be reduced to half to an observer in frame S?.
A circular lamina moves with its plane parallel to the x-y plane of a reference frame S at rest. Assuming its motion to be along the axis of x (or y), calculate the velocity at which surface area would appear to be reduced to half to an observer in frame S? for Teaching 2024 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about A circular lamina moves with its plane parallel to the x-y plane of a reference frame S at rest. Assuming its motion to be along the axis of x (or y), calculate the velocity at which surface area would appear to be reduced to half to an observer in frame S? covers all topics & solutions for Teaching 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular lamina moves with its plane parallel to the x-y plane of a reference frame S at rest. Assuming its motion to be along the axis of x (or y), calculate the velocity at which surface area would appear to be reduced to half to an observer in frame S?.
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