The M.I. of a body about the given axis is 1. | vedclass

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

Question

(B) Given: Moment of Inertia $I = 1.2 \, kg \cdot m^2$,Initial angular velocity $\omega_0 = 0$,Rotational Kinetic Energy $K_r = 1500 \, J$,Angular acc

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Given: Moment of Inertia $I = 1.2 \, kg \cdot m^2$,Initial angular velocity $\omega_0 = 0$,Rotational Kinetic Energy $K_r = 1500 \, J$,Angular acceleration $\alpha = 25 \, rad/s^2$.Step $1$: Calculate the final angular velocity $\omega$ using the formula for rotational kinetic energy:$K_r = \frac{1}{2} I \omega^2$$1500 = \frac{1}{2} 	imes 1.2 	imes \omega^2$$1500 = 0.6 	imes \omega^2$$\omega^2 = \frac{1500}{0.6} = 2500$$\omega = \sqrt{2500} = 50 \, rad/s$.Step $2$: Calculate the time $t$ required using the kinematic equation $\omega = \omega_0 + \alpha t$:$50 = 0 + 25 	imes t$$t = \frac{50}{25} = 2 \, s$.

The $M.I.$ of a body about the given axis is $1.2 \, kg \cdot m^2$ and initially the body is at rest. In order to produce a rotational kinetic energy of $1500 \, J$,an angular acceleration of $25 \, rad/s^2$ must be applied about that axis for a duration of ........ $s$.

Similar Questions

$A$ wheel is rotating with an angular speed of $20\ rad/s$. 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 $0.20\ kg\cdot m^2$,then the work done by the torque in two seconds will be .......... $J$.

$A$ uniform rod of mass $M$ and length $L$ is pivoted at one end and is free to rotate in a vertical plane. The rod is released from rest in a horizontal position. What is the angular velocity of the rod when it reaches the vertical position?

The power $(P)$ is supplied to a rotating body having moment of inertia '$I$' and angular acceleration '$\alpha$'. Its instantaneous angular velocity is

$A$ thin rod of mass $m$ and length $l$ is oscillating about a horizontal axis through its one end. Its maximum angular speed is $\omega$. Its centre of mass will rise up to a maximum height of:

$A$ tangential force $F$ is applied on the rim of a ring of radius $R$. If the ring rotates by an angle $\theta$,what is the work done by the force?

Vedclass Test Series

Exam Paper Generator

Online Exam Module