A body rotating with an angular velocity of 3 | vedclass

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

Question

(A) The rotational kinetic energy $(K_{rot})$ of the rotating body is given by $K_{rot} = \frac{1}{2} I \omega^2$. Given $I = 3 \ kg \cdot m^2$ and $\

Vedclass · Accepted Answer

$1.0$

Vedclass · Answer

(A) The rotational kinetic energy $(K_{rot})$ of the rotating body is given by $K_{rot} = \frac{1}{2} I \omega^2$. Given $I = 3 \ kg \cdot m^2$ and $\omega = 3 \ rad/s$,we have: $K_{rot} = \frac{1}{2} 	imes 3 	imes (3)^2 = \frac{1}{2} 	imes 3 	imes 9 = 13.5 \ J$. The translational kinetic energy $(K_{trans})$ of the second body is given by $K_{trans} = \frac{1}{2} m v^2$. Given $m = 27 \ kg$ and $K_{trans} = K_{rot} = 13.5 \ J$,we have: $\frac{1}{2} 	imes 27 	imes v^2 = 13.5$. $v^2 = \frac{13.5 	imes 2}{27} = \frac{27}{27} = 1$. Therefore,$v = 1 \ m/s$.

Similar Questions

If a body completes one revolution in $\pi \ s$,then the moment of inertia is related to the rotational kinetic energy $(K)$ by which of the following expressions?

Two bodies have their moments of inertia $I$ and $2I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal,their angular momentum will be in the ratio

An energy of $484\,J$ is spent in increasing the speed of a flywheel from $60\,rpm$ to $360\,rpm$. The moment of inertia of the flywheel is $.............\,kg\cdot m^2$.

Three particles are situated on a light and rigid rod along the $Y$-axis as shown in the figure. If the system is rotating with an angular velocity of $2 \, rad/s$ about the $X$-axis,then the total kinetic energy of the system is ...... $J$.

$A$ flywheel rotating about a fixed axis has a kinetic energy of $360 \ J$ when its angular speed is $30 \ rad/s$. The moment of inertia of the wheel about the axis of rotation is ...... $kg \ m^2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module