Find the radius of an equilateral triangular plate about its median. Side of triangular is l.

Options

A. `l/(sqrt12)`
B. `l/(sqrt(24))`
C. `l/(sqrt(96))`
D. `l/(sqrt48)`

Answer

B

Explanation

`dm=M/((sqrt(3)t^(2))/4)xx(2y)/(sqrt(3))dy`
`dI=1/12xxdm((2y)/(sqrt(3)))^(2)`
`=1/12xx(2Mydy)/(3l^(2))xx(4y^(2))/3`
`=(32M)/(27l^(2))/int_(0)^(lsqrt(3)//2)y^(3)dy=M/(27l^(2))xx1/4xx((lsqrt(3))/2)^(4)`
`=M/(27xx2l^(2l))xx(lxx9)/16=(Ml^(2))/24`