Ratio of the ranges of the bullets fired from a gun `(` of constant muzzle speed `)` at angle `theta, 2 theta &4 theta` is found in the ratio `x:2:2`, then the value of `x` will be `(` Assume same muzzle speed of bullets `)`

Options

A. 1
B. 2
C. `sqrt(3)`
D. none of these

Answer

D

Explanation

Range is same for `2 theta` and `4 theta`.
`:. 4 theta+4 theta=90^(@)rArrtheta 15^(@)`
`:. ` Ratio of ranges will be sin `30^(@): sin60^(@):sin120^(@)`.
`(1)/(2):(sqrt(3))/(2):(sqrt(3))/(2)rArr(2)/(sqrt(3)):2:2`