Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm ), about its axis be I. the radius of a thin cylinder of the same about its axis is also I is :

Options

A. 16 cm
B. 18 cm
C. 14 cm
D. 12 cm

Answer

A

Explanation

`rho` = density `1/2MR^(2) -1/2mr^(2) = (M-m)K`
`rArr 1/2rho pi R^(2) -1/2rho pir^(2)r^(2) =(M-m)K^(2)`
`rArr 1/2rho pi R^(2) R^(2) -1/2rho pi r^(2) r^(2) =(M-m)K^(2)`
`rArr (pi rho)/2(R^(4)-r^(4))= rho pi(R^(2)-r^(2))K^(2)`
`rArr (R^(2) + r^(2))/2 = K^(2)`
`rArr K= sqrt((R theta)2 + 10^(2))/2 = sqrt(250) = 15.81 ~~ 16 m`