A uniform thin rod of length l and mass m is | vedclass

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

Question

(A) The moment of inertia of a uniform thin rod of mass $m$ and length $l$ about an axis passing through one of its ends is given by $I = \frac{1}{3}m

Vedclass · Accepted Answer

$\frac{2}{3}{\pi ^2}{f^2}m{l^2}$

Vedclass · Answer

(A) The moment of inertia of a uniform thin rod of mass $m$ and length $l$ about an axis passing through one of its ends is given by $I = \frac{1}{3}ml^2$.The angular velocity $\omega$ in terms of frequency $f$ is given by $\omega = 2\pi f$.The rotational kinetic energy $K$ is given by the formula $K = \frac{1}{2}I\omega^2$.Substituting the values of $I$ and $\omega$ into the formula:$K = \frac{1}{2} 	imes (\frac{1}{3}ml^2) 	imes (2\pi f)^2$$K = \frac{1}{6}ml^2 	imes 4\pi^2 f^2$$K = \frac{2}{3}\pi^2 f^2 ml^2$.Thus,the correct option is $A$.

$A$ uniform thin rod of length $l$ and mass $m$ is suspended from one of its ends and is rotated at $f$ rotations per second. The rotational kinetic energy of the rod will be

Similar Questions

$A$ body is rotating about its own axis. Its rotational kinetic energy is $x$ and its angular momentum is $y$. Hence,its moment of inertia about its own axis is:

$A$ circular disc of mass $20 \ kg$ and radius $1 \ m$ is rotating about an axis passing through its center and perpendicular to its plane with an angular velocity of $2 \ rad \ s^{-1}$. Then the rotational kinetic energy of the disc is (in $J$)

$A$ thin circular disc of mass $12 \,kg$ and radius $0.5 \,m$ rotates with an angular velocity of $100 \,rad/s$. The rotational kinetic energy of the disc is (in $\,kJ$)

The rotational kinetic energy and translational kinetic energy of a rolling body are the same. The body is:

$A$ 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 ....... $J$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module