The moment of inertia of a body about a given axis is 2.4 kg - m 2 . To produce a rotational kinetic energy of 750 J, an angular acceleration of a 5 rad / s 2 must be applied about that axis for:

Question

The moment of inertia of a body about a given axis is 2.4 kg - m 2 . To produce a rotational kinetic energy of 750 J, an angular acceleration of a 5 rad / s 2 must be applied about that axis for: (A) 3 s (B) 4 s (C) 5 s (D) 6 s

Tardigrade Admin · Accepted Answer

Kinetic energy of rotation is half the product of the moment of inertia

(I)

of the body and square of the angular velocity

(ω)

of the body.

∴ d K = \frac{1}{2} I ω^{2}

Given,

I = 2.4 k g - m^{2},

K = 750 J

\Rightarrow ω^{2} = \frac{2 K}{I}

= \frac{2 \times 750}{2.4} = 625

\Rightarrow ω = 25 r a d / s .

Also angular acceleration

(α) \times

time

(t) =

angular velocity

(ω)

\Rightarrow t = \frac{ω}{α} = \frac{25}{5} = 5 s .

Q. The moment of inertia of a body about a given axis is 2.4kg−m2. To produce a rotational kinetic energy of 750J, an angular acceleration of a 5rad/s2 must be applied about that axis for:

3 s

4 s

5 s

6 s

Q. The moment of inertia of a body about a given axis is $2.4 k g - m^{2} .$ To produce a rotational kinetic energy of $750 J$ , an angular acceleration of a $5 r a d / s^{2}$ must be applied about that axis for: