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If the sum of the circumferences of two circles with radii \[R1\] and \[R2\] is equal to the circumference of a circle of radius \[R\], then (A) \[{{R}_{1}}+{{R}_{2}}=R\] (B) \[{{R}_{1}}+{{R}_{2}}>R\] (C) \[{{R}_{1}}+{{R}_{2}}<R\] (D) Nothing definite can be said about the relation among \[{{R}_{1}}\], \[{{R}_{2}}\] & \[R\].
If the sum of the circumferences of two circles with radii \[R1\] and \[R2\] is equal to the circumference of a circle of radius \[R\], then (A) \[{{R}_{1}}+{{R}_{2}}=R\] (B) \[{{R}_{1}}+{{R}_{2}}>R\] (C) \[{{R}_{1}}+{{R}_{2}}<R\] (D) Nothing definite can be said about the relation among \[{{R}_{1}}\], \[{{R}_{2}}\] & \[R\].
Areas Related to Circles | Exercise 11.1 | Maths | NCERT Exemplar
If the sum of the circumferences of two circles with radii \[R1\] and \[R2\] is equal to the circumference of a circle of radius \[R\], then (A) \[{{R}_{1}}+{{R}_{2}}=R\] (B) \[{{R}_{1}}+{{R}_{2}}>R\] (C) \[{{R}_{1}}+{{R}_{2}}<R\] (D) Nothing definite can be said about the relation among \[{{R}_{1}}\], \[{{R}_{2}}\] & \[R\].

The Correct option(A) \[{{R}_{1}}+{{R}_{2}}=R\]

Explanation:

From the given question,

We got sum of the circumferences of two circles with radii \[R1\] and \[R2\] is equal to the circumference of a circle of radius \[R\]

That is Circumference of circle with radius \[R\] = Circumference of first circle with radius  \[{{R}_{1}}\] + Circumference of second circle with radius \[{{R}_{2}}\]

Therefore \[2\pi R=2\pi {{R}_{1}}+2\pi {{R}_{2}}\]

We got  \[{{R}_{1}}+{{R}_{2}}=R\]

Therefore  Option A is correct.

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More Material

(i) Consider a thin lens placed between a source (S) and an observer (O). Let the thickness of the lens vary as 2 0 () – α = b wb w, where b is the verticle distance from the pole. w0 is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.
(ii) A gravitational lens may be assumed to have a varying width of the form w(b) = k1 ln (k2/b) = k1 ln (k2/bmin). Show that an observer will see an image of a point object as a ring about the centre of the lens with an angular radius.
β = √(n-1)k1 u/v / u + v

If light passes near a massive object, the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refractive index of the medium given by n(r) = 1 + 2 GM/rc2 where r is the distance of the point of consideration from the centre of the mass of the massive body, G is the universal gravitational constant, M the mass of the body and c the speed of light in vacuum. Considering a spherical object find the deviation of the ray from the original path as it grazes the object.