The curvature of circle depends inversely upon its radius r
True or fals
Answers
TRUE : The curvature of circle depends inversely upon its radius r
Step-by-step explanation:
At every point on a circle, the curvature is the reciprocal of the radius
The curvature measures how fast a curve is changing direction at a given point
the radius of curvature, R, is the reciprocal of the curvature.
x² + y² = r²
=> 2x + 2y dy/dx = 0
=> dy/dx = - x/y
d²y/dx² = - x (-1/y²)dy/dx - 1/y
=> d²y/dx² = (x/y²)(-x/y) - 1/y
=> d²y/dx² = (-1/y³)(x² + y²)
R = ( 1 + (dy/dx)²)^(3/2) / |(d²y/dx²)|
=> R = ( 1 + (- x/y)²)^(3/2) / |(-1/y³)(x² + y²)|
=> R = (y² + x²)^(3/2)/(x² + y²)
=> R = √(x² + y²)
=> R = √r²
=> R = r
The curvature of circle depends inversely upon its radius r is TRUE
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