A uniform solid cone of height H is cut at a distance x below its vertex, parallel to its base and the upper part is discarded. The CM. of the remaining part is found to be 50% lower, w.r.t. to the base. The ratio, `r =x/H` satisfies.

Options

A. `7r^(3) - 8r^(4) =1`
B. `r = 1/2^(1//3)`
C. `r =1/2`
D. `7r^(3) - 6r^(4) =1`

Answer

D

Explanation

The final CM. is at `H/8` above the base. The volume, and consequently the mass of a cone (of fixed vertical angle) is proportional to the cube of its height. Taking the origin at apex. `(7H)/8 = (H^(3) (3H)/4 - x^(3) (3x)/4)/(H^(3) -x^(3))`
Rearranging, we get the required condition.