A constant external torque `tau` acts for a very brief period `Delta t` on a rotating system having moment of inertia `I`.
(`i`) The angular momentum of the system will change by `tau Delta t`
(`ii`) The angular velocity of the system will change by `(tau Delta t)//I`.
(`iii`) If the system was initially at rest, it will acquire rotational kinetic energy `(tau Delta t)^(2)//2I`.
(`iv`) The kinetic energy of the system will change by `(tau Delta t)^(2) I`.

Options

A. (`i`),(`ii`)
B. (`i`),(`ii`),(`iii`)
C. (`ii`),(`iv`)
D. (`i`),(`iii`),(`iv`)

Explanation

`Delta L= tau Delta t`
`I Delta omega= tau Delta timplies Delta omega=(tau Delta t)/(I)`
`Delta omega= omega-0=(tau Delta t)/(I)`
`K_(R)=(1)/(2)Iomega^(2)=(1)/(2)I((tau Delta t)/(I))^(2)=((tau Delta t)^(2))/(2I)`