A solid cylinder of mass M and radius R is ro | vedclass

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

Question

(B) The moment of inertia of a solid sphere about its diameter is $I_S = \frac{2}{5} M R^2$. The moment of inertia of a solid cylinder about its geome

Vedclass · Accepted Answer

$1: 5$

Vedclass · Answer

(B) The moment of inertia of a solid sphere about its diameter is $I_S = \frac{2}{5} M R^2$. The moment of inertia of a solid cylinder about its geometrical axis is $I_C = \frac{1}{2} M R^2$. Let $\omega_C$ be the angular speed of the cylinder and $\omega_S$ be the angular speed of the sphere. Given that $\omega_S = \frac{\omega_C}{2}$. The rotational kinetic energy is given by $K.E. = \frac{1}{2} I \omega^2$. The ratio of the kinetic energy of the sphere to that of the cylinder is: $\frac{K.E._S}{K.E._C} = \frac{\frac{1}{2} I_S \omega_S^2}{\frac{1}{2} I_C \omega_C^2} = \frac{I_S}{I_C} 	imes \left( \frac{\omega_S}{\omega_C} ight)^2$. Substituting the values: $\frac{K.E._S}{K.E._C} = \frac{\frac{2}{5} M R^2}{\frac{1}{2} M R^2} 	imes \left( \frac{\omega_C / 2}{\omega_C} ight)^2 = \frac{2/5}{1/2} 	imes \left( \frac{1}{2} ight)^2 = \frac{4}{5} 	imes \frac{1}{4} = \frac{1}{5}$. Thus,the ratio is $1: 5$.

Similar Questions

In the given figure,two wheels $P$ and $Q$ are connected by a belt $B$. The radius of $P$ is three times as that of $Q$. In case of same rotational kinetic energy,the ratio of rotational inertias $\left(\frac{I_{P}}{I_{Q}}\right)$ will be $x: 1$. The value of $x$ will be $.....$ .

Write the formula for rotational kinetic energy.

Two objects have moments of inertia $I_1$ and $I_2$ $(I_1 > I_2)$ and their angular velocities are equal. If their rotational kinetic energies are $E_1$ and $E_2$ respectively,then:

$A$ flywheel is making $\frac{3000}{\pi}$ revolutions per minute about its axis. If the moment of inertia of the flywheel about that axis is $400 \ kg \ m^2$,its rotational kinetic energy is

Vedclass Test Series

Exam Paper Generator

Online Exam Module