A coil of radius R carries a current `I`. Another concentric coil of radius `r (r lt lt R)` carries current `(1)/(2)`. Initially planes of the two coils are mutually prependicular and both the coil are free to rotate about common diameter. They are released from rest from this position. The masses of the coils are M and m respectively. `(m lt M)`. During the subsequeny motion let `K_(1)` and `K_(2)` be the maximum kinetic energies of the two cells respectively. and let U be the magnetic of maximum potential energy of magnetic interaction of the system of the coils. Choose the correct options.

Options

A. `(K_(1))/(K_(2))=(M)/(m)((R)/(r))^(2)`
B. `K_(1)=(Umr^(2))/(mr^(2)+MR^(2))K_(2)=(UMR^(2))/(mr^(2)+MR^(2))`
C. `U=(mu_(0)pi l^(2)r^(2))/(4R)`
D. `K_(2)gt gt K_(1)`

Answer

B, C, D

Explanation

`tau_(1)=tau_(2)rArr (int tau dt)/(I) =omega rArr omega prop (1)/(I)`
`K.E =(1)/(2) I omega^(2) prop (1)/(I)`
`(K_(1))/(K_(2))=((mr^(2))/(2))/((MR^(2))/(2))rArr (K_(1))/(K_(2))=(m)/(M)((r)/(R))^(2)`
`K_(1)+K_(2)=U rArr K_(2)(m)/(M)((r)/(R))^(2)+K_(2)=U`
`K_(2)=(UMR^(2))/(mr^(2)+MR^(2))rArr K_(1)=(Umr^(2))/(mr^(2)+MR^(2))`
`U=(I)/(2)pi r^(2)(mu_(0)I)/(2R)=(mu_(0)I^(2)pi r^(2))/(4R)`