Question

8.
A body of M.I. of 3 kg-m², rotating with an angular
velocity of 2 rad/s, has the same K.E. as a mass of 12 kg
moving with a velocity of
(a) 8 m/s
(b) 4 m/s
(c) 2 m/s
(d) 1 m/s​

Answer 1

$\huge\underline{\underline{\bf \orange{Question-}}}$

A body of M.I. of 3 kg-m², rotating with an angular

velocity of 2 rad/s, has the same K.E. as a mass of 12 kg moving with a velocity of

$\huge\underline{\underline{\bf \orange{Solution-}}}$

$\large\underline{\underline{\sf Given:}}$

• Moment of inertia (I) = 3 kg-m²
• Angular Velocity ${\sf (\omega)}$ = 2 rad/s
• Mass (m) = 12kg

$\large\underline{\underline{\sf To\:Find:}}$

• Velocity (v)

$\large\implies{\bf \blue{\dfrac{1}{2}I\omega^2=\dfrac{1}{2}mv^2}}$

$\implies{\sf \dfrac{1}{2}×3×(2)^2=\dfrac{1}{2}×12×v^2}$

$\implies{\sf \dfrac{1}{2}×6=\dfrac{1}{2}×6v^2 }$

$\implies{\sf v^2=\dfrac{6}{6}}$

$\implies{\bf \red{Velocity (v)=1m/s}}$

$\huge\underline{\underline{\bf \orange{Solution-}}}$

Velocity is ${\bf\red{1\:m/s}}$.

Answer 2

Answer:

Option d

1 m/s

is the answer