A meter stick is held vertically with one end | vedclass

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

Question

(B) Let the length of the meter stick be $L = 1 \, m$ and its mass be $m$.Initially,the center of mass is at height $h = L/2 = 0.5 \, m$.By the princi

Vedclass · Accepted Answer

$5.4$

Vedclass · Answer

(B) Let the length of the meter stick be $L = 1 \, m$ and its mass be $m$.Initially,the center of mass is at height $h = L/2 = 0.5 \, m$.By the principle of conservation of energy,the loss in potential energy equals the gain in rotational kinetic energy.$mgh = \frac{1}{2} I \omega^2$Since the stick rotates about the end on the floor,the moment of inertia $I = \frac{mL^2}{3}$.$mg(L/2) = \frac{1}{2} (\frac{mL^2}{3}) \omega^2$$gL = \frac{L^2}{3} \omega^2 \Rightarrow \omega^2 = \frac{3g}{L}$$\omega = \sqrt{\frac{3g}{L}} = \sqrt{3 	imes 9.8} = \sqrt{29.4} \approx 5.42 \, rad/s$.The linear speed of the other end is $v = \omega L = \sqrt{3gL} = \sqrt{3 	imes 9.8 	imes 1} = \sqrt{29.4} \approx 5.42 \, m/s$.Rounding to one decimal place,the speed is $5.4 \, m/s$.

$A$ meter stick is held vertically with one end on the floor and is allowed to fall. The speed of the other end when it hits the floor,assuming that the end at the floor does not slip,is ......... $m/s$ $(g = 9.8 \, m/s^2)$.

Similar Questions

$A$ particle executes uniform circular motion with angular momentum $L$. Its rotational kinetic energy becomes half,when the angular frequency is doubled. Its new angular momentum is

$Assertion$ : $A$ helicopter must necessarily have two propellers.
$Reason$ : Two propellers are provided in a helicopter in order to conserve linear momentum.

$A$ particle is moving in a uniform circular motion with angular momentum $L$. If its angular frequency is doubled and its kinetic energy is halved,then the new angular momentum of the particle will be .......

Four spheres,each of mass $M$ and diameter $2a$,are placed at the corners of a square of side $b$. The moment of inertia of this system about an axis along one of the sides of the square is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module