Question

The two torsion pendula differ only by the addition of cylindrical masses as shown in the figure. The radius of each additional mass is `1//4` the radius fo the disc. Each cylinder and disc have equal mass. The ratio of time periods of the two torsion pendula is `p`. Then `27 p^(2) ` is.

Answer 1

`I_(1) = (MR^(2))/(2)`
`I_(2) = [M/2(R/4)^(2) + M((3R)/4)^(2)] + [M/2(R/4)^(2) + M((3R)/4)^(2)] + (MR^(2))/(2)`
`T prop sqrt(1)`
`(T_(1))/(T_(2)) prop sqrt((I_(1))/(I_(2)))`