Question

The moment of inertia of a body initially at rest about a given axis is 1.2 kg m². On applying an acceleration of 25 rad/s², the time it will take to acquire a rotational kinetic energy of 1500 J is ____________.

Options

• 4 s

• 2 s

• 8 s

• 10 s

Answer 1

The moment of inertia of a body initially at rest about a given axis is 1.2 kg m². On applying an acceleration of 25 rad/s², the time it will take to acquire a rotational kinetic energy of 1500 J is 2 s.

Explanation:

`"Rotational kinetic energy" = 1/2 "I" omega^2`

`"Given"  1500 = 1/2 "I" (omega/"t" xx "t")^2`

`Rightarrow 1500 = 1/2 "I" (alpha xx "t")^2            [because omega/"t" = alpha]`

`Rightarrow "t"^2 = 3000/("I" alpha^2)`

` = 3000/1.2 xx 625`

` = 4  "s"`

`therefore "t" = 2  "s"`