A solid sphere of mass m and radius R is rota | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The rotational kinetic energy is given by $E = \frac{1}{2} I \omega^2$.For the solid sphere rotating about its diameter,the moment of inertia is $

Vedclass · Accepted Answer

$1:5$

Vedclass · Answer

(D) The rotational kinetic energy is given by $E = \frac{1}{2} I \omega^2$.For the solid sphere rotating about its diameter,the moment of inertia is $I_s = \frac{2}{5} m R^2$.For the solid cylinder rotating about its geometrical axis,the moment of inertia is $I_c = \frac{1}{2} m R^2$.Given that the angular speed of the cylinder is twice that of the sphere,we have $\omega_c = 2 \omega_s$.The ratio of their kinetic energies is:$\frac{E_{sphere}}{E_{cylinder}} = \frac{\frac{1}{2} I_s \omega_s^2}{\frac{1}{2} I_c \omega_c^2} = \frac{I_s \omega_s^2}{I_c (2 \omega_s)^2} = \frac{I_s}{4 I_c}$.Substituting the values of $I_s$ and $I_c$:$\frac{E_{sphere}}{E_{cylinder}} = \frac{\frac{2}{5} m R^2}{4 	imes \frac{1}{2} m R^2} = \frac{2/5}{2} = \frac{1}{5}$.Thus,the ratio is $1:5$.

Similar Questions

If the angular velocity of a body rotating about a given axis increases by $20 \%$,then its kinetic energy of rotation will increase by: (in $\%$)

Two bodies $A$ and $B$ are rotating freely with moments of inertia $I_A$ and $I_B$ respectively. Given $I_A > I_B$ and their angular momenta are equal. If $K_A$ and $K_B$ are their rotational kinetic energies,then:

$A$ molecule consists of two atoms each of mass $m$ and separated by a distance $d$. At room temperature,the average rotational kinetic energy is $E$. What is its angular frequency?

$A$ flywheel of moment of inertia $0.32 \ kg \cdot m^2$ is rotated steadily at $120 \ rad/s$ by a $50 \ W$ electric motor. The kinetic energy of the flywheel is .......... $J$.

Two rotating bodies $A$ and $B$ of masses $m$ and $2m$ with moments of inertia $I_A$ and $I_B$ $(I_B > I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ are their angular momenta respectively,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module