A circular ring of radius 3cm hangs horizontally from a point 4 cm vertically above the centre by 4 strings attached at equal intervals to its circumference. If the angle between two consecutive strings be `theta` , then `costheta` is equal to (A)`4/5` (B) `4/(25)` (C) `(16)/(25)` (D) none of these

Options

A. `4/5`
B. `4/25`
C. `16/25`
D. none of these

Answer

C

Explanation

Let O be the centre of the circular ring which is suspended by the strings PA, PB, PC and PD in such a way that P is just above the point O and arcAB=arcBC=arcCD=arcAD.

`therefore angleAOB=90^@`
Also, in `triangleAOP`, we have
`AP=sqrt(OA^2+OP^2)=sqrt(3^2+4^2)=5`
`rArr` BP=AP=5
In `triangleAPB` , we have
`cos theta=(AP^2 +BP^2 -AB^2)/(2 AP.BP)`
`rArr cos theta=(5^2+5^2 -(3sqrt2)^2)/(2xx5xx5)[ "In" triangleAOB, AB^2=OA^2+OB^2]`
`rArr cos theta=16/25`