Question

12.
A uniform solid sphere of mass 0.5 kg and
radius 5 cm is rotating about an axis through its
centre at an angular speed of 10 rad's. Its
rotational kinetic energy is
(A) 0.025 J
(B) 0.5 J
(C)1.5J
(D) 2.5
​

Answer 1

Answer:

Rotational Kinetic energy=1/2Iω²

                                          =1/2*0.5*0.05²*10²

                                           =1/2*0.05*0.0025*100

                                           =50*0.05*0.0025

                                            =0.00625 J

PLEASE MARK IT AS BRAINLIEST IF IT HELPS YOU

Answer 2

$\displaystyle\Large\boxed {\sf {(A)\quad\!0.025\ J}}$

Given,

• $\displaystyle\sf {M=0.5\ kg}$

• $\displaystyle\sf {R=5\times10^{-2}\ m}$

• $\displaystyle\sf{\omega=10\ rad\ s^{-1}}$

Then, rotational kinetic energy,

$\displaystyle\longrightarrow\sf{K_r=\dfrac {1}{2}I\omega^2}$

For a solid sphere, $\displaystyle\sf {I=\dfrac {2}{5}\ MR^2}$

$\displaystyle\longrightarrow\sf{K_r=\dfrac {1}{2}\cdot\dfrac {2}{5}\ MR^2\cdot \omega^2}$

$\displaystyle\longrightarrow\sf{K_r=\dfrac {1}{5}\times0.5\times(5\times10^{-2})^2\times10^2}$

$\displaystyle\longrightarrow\sf{\underline {\underline {K_r=0.025\ J}}}$