If the rotational kinetic energy of a body is | vedclass

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

Question

(C) The rotational kinetic energy $E$ and angular momentum $L$ are related by the formula $E = \frac{L^2}{2I}$,where $I$ is the moment of inertia.This

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(C) The rotational kinetic energy $E$ and angular momentum $L$ are related by the formula $E = \frac{L^2}{2I}$,where $I$ is the moment of inertia.This implies $L = \sqrt{2IE}$,so $L \propto \sqrt{E}$.Let the initial kinetic energy be $E_1 = E$.The new kinetic energy $E_2$ is increased by $300\ \%$,so $E_2 = E + 300\% 	ext{ of } E = E + 3E = 4E$.The ratio of the new angular momentum $L_2$ to the initial angular momentum $L_1$ is $\frac{L_2}{L_1} = \sqrt{\frac{E_2}{E_1}} = \sqrt{\frac{4E}{E}} = 2$.Thus,$L_2 = 2L_1$.The percentage increase in angular momentum is given by $\frac{L_2 - L_1}{L_1} 	imes 100\ \% = \frac{2L_1 - L_1}{L_1} 	imes 100\ \% = 100\ \%$.

If the rotational kinetic energy of a body is increased by $300\ \%$,then the percentage increase in its angular momentum will be .......... $\%$

Similar Questions

$A$ spherical solid ball of $10\,kg$ mass and radius $3\,cm$ is rotating about an axis passing through its centre with an angular velocity of $50\,rad/s$. The kinetic energy of rotation is ....... $J$.

$A$ solid cylinder of mass $20 \; kg$ rotates about its axis with angular speed $100 \; rad \; s^{-1}$. The radius of the cylinder is $0.25 \; m$. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

$A$ spherical solid ball of $1\,kg$ mass and radius $30\,cm$ is rotating about an axis passing through its centre with an angular velocity of $50\,rad/s$. The kinetic energy of rotation is ......... $J$.

Two rotating bodies $P$ and $Q$ of masses $m$ with moment of inertia $I_P$ and $I_Q$ $(I_Q > I_P)$ have equal kinetic energy of rotation. If $L_P$ and $L_Q$ are their angular momenta respectively,then:

The moments of inertia of two bodies about their axes of rotation are $I$ and $2I$ respectively. If their rotational kinetic energies are equal,what is the ratio of their angular velocities?

Vedclass Test Series

Exam Paper Generator

Online Exam Module