Question
Three balls of equal radius are placed such that they are touching each other. A fourth smaller ball is kept such that it touches the other three.Find the ratio of the radii of smaller to larger ball.
Answer: Option A
:
A
Option (a)
Let the centers of the large balls be x, y, z and radius R.
O is the centre of the smaller ball and radius r...
x, y, z form an equilateral triangle with side equal to 2R.
O is the centroid of this triangle.
Therefore ox=oy=oz=R+r= 23(height of the triangle xyz)
Height=(√32)(2R) =√3R
Therefore R+r = 23(√3R) ⇒ rR = (2−√3)√3
Shortcut:- Using the approximation technique used in class, the radius of the bigger circle: smaller circle is close to 0.2.
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:
A
Option (a)
Let the centers of the large balls be x, y, z and radius R.
O is the centre of the smaller ball and radius r...
x, y, z form an equilateral triangle with side equal to 2R.
O is the centroid of this triangle.
Therefore ox=oy=oz=R+r= 23(height of the triangle xyz)
Height=(√32)(2R) =√3R
Therefore R+r = 23(√3R) ⇒ rR = (2−√3)√3
Shortcut:- Using the approximation technique used in class, the radius of the bigger circle: smaller circle is close to 0.2.
Was this answer helpful ?
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