If angular momentum of a rotating body is increased by 200 % , then its kinetic energy of rotation w

English

Gujarati

Hindi

6.System of Particles and Rotational Motion

medium

If the angular momentum of a rotating body is increased by $200\ \%$, then its kinetic energy of rotation will be increased by .......... $\%$

A

$400$

B

$ 800$

C

$200$

D

$ 100$

Solution

As $E = \frac{{{L^2}}}{{2I}}$

$\frac{{{E_2}}}{{{E_1}}} = {\left( {\frac{{{L_2}}}{{{L_1}}}} \right)^2}$$ = {\left( {\frac{{3{L_1}}}{{{L_1}}}} \right)^2}$

[As ${L_2} = {L_1} + 200\% \,.{L_1} = 3L_1$]

${E_2} = 9{E_1}$$ = {E_1} + 800\% $ of ${E_1}$

Standard 11

Physics

Share

Similar Questions

A wheel of moment of inertia $10\ kg-m^2$ is rotating at $10$ rotations per minute. The work done in increasing its speed to $5$ times its initial value, will be………. $J$

medium

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy $(K_t)$ as well as rotational kinetic energy $(K_r)$ simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere is

medium

(AIPMT-1991)

A student of mass $M$ is $1.5 \,m$ tall and has her centre of mass $1 \,m$ above ground when standing straight. She wants to jump up vertically. To do so. she bends her knees so that her centre of mass is lowered by $0.2 \,m$ and then pushes the ground by a constant force F. As a result, she jumps up such that the maximum height of her feet is $0.3 \,m$ above ground. The ratio $F / Mg$ is

normal

(KVPY-2021)

A wheel is rotating with an angular speed of $20\,rad/sec$. It is stopped to rest by applying a constant torque in $4\ s$. If the moment of inertia of the wheel about its axis is $0.20\ kg-m^2$, then the work done by the torque in two seconds will be ………. $J$

medium

Which of the following (if mass and radius are assumed to be same) have maximum percentage of total $K.E.$ in rotational form while pure rolling?

medium