A straight rod of length L is released on a f | vedclass

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

Question

(B) Let the rod be of length $L$. The lower end of the rod is at the origin $(0,0)$ initially. The center of mass of the rod is at $(0, L/2)$.As the r

Vedclass · Accepted Answer

$L/4$

Vedclass · Answer

(B) Let the rod be of length $L$. The lower end of the rod is at the origin $(0,0)$ initially. The center of mass of the rod is at $(0, L/2)$.As the rod falls,the center of mass moves vertically downwards to the point $(0,0)$ on the floor.Let a point $P$ be at a distance $x$ from the lower end of the rod.Initially,the coordinates of point $P$ are $(0, x)$.When the rod falls and lies flat on the floor,the lower end is at a distance $L$ from the origin,and the center of mass is at the origin $(0,0)$.In the final horizontal position,the point $P$ is at a distance $(L-x)$ from the origin (the center of mass position).For the point $P$ to trace a circular path of radius $r$,its distance from the center of mass (which acts as the center of rotation for the rod's motion) must remain constant.Initially,the distance of $P$ from the center of mass is $r = |L/2 - x|$.Finally,when the rod is horizontal,the distance of $P$ from the center of mass is $r = |L - x - L/2| = |L/2 - x|$.For the path to be a quarter circle,the vertical displacement must equal the horizontal displacement. The point $P$ starts at height $x$ and ends at horizontal distance $L-x$ from the initial base.Setting $x = L/2 - x$ (distance from center of mass),we get $2x = L/2$,which implies $x = L/4$.

$A$ straight rod of length $L$ is released on a frictionless horizontal floor in a vertical position. As it falls and slips,the distance of a point on the rod from the lower end,which follows a quarter circular locus,is

Similar Questions

$A$ massless string is wrapped around a disc of mass $M$ and radius $R$. Another end is tied to a mass $m$ which is initially at height $h$ from the ground level as shown in the figure. If the mass is released,then its velocity while touching the ground level will be:

For a rigid body in rotational motion,if a particle at a distance of $5 \, cm$ from the axis of rotation has an angular velocity of $10 \, rad/s$,what is the linear velocity of a particle at a distance of $10 \, cm$ from the axis of rotation (in $, cm/s$)?

For the given figure,find the acceleration of the $1\, kg$ block. The string is massless,the mass of the pulley is $M = 2\, kg$,and the diameter of the pulley is $0.2\, m$. (in $m/s^2$)

What is the value of linear velocity if $\overrightarrow{r} = 3\widehat{i} + 4\widehat{j} + 6\widehat{k}$ and $\overrightarrow{\omega} = -5\widehat{i} + 3\widehat{j} + 5\widehat{k}$?

The instantaneous velocity of point $B$ of a rod of length $L = 0.5 \ m$ is $v = 3 \ m/s$ at an angle of $30^{\circ}$ with the rod as shown. The angular velocity of the rod for the minimum velocity of end $A$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module