A disc of mass m and radius R is attached to | vedclass

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

Question

(A) The disc is suspended by two parallel ropes of length $l$. When the disc is displaced slightly in its own plane,it undergoes a motion similar to a

Vedclass · Accepted Answer

$2\pi \sqrt {\frac{l}{g}}$

Vedclass · Answer

(A) The disc is suspended by two parallel ropes of length $l$. When the disc is displaced slightly in its own plane,it undergoes a motion similar to a physical pendulum.For a physical pendulum,the time period is given by $T = 2\pi \sqrt{\frac{I}{mgd}}$,where $I$ is the moment of inertia about the axis of rotation and $d$ is the distance from the pivot to the center of mass.In this case,the ropes are attached at a distance $R/2$ above the center of the disc. The effective length of the pendulum is $l_{eff} = l$. However,because the ropes are attached at the rim (or specific points),the disc swings such that the center of mass moves in an arc of radius $l$.Since the ropes remain parallel during the motion,the disc does not rotate about its center of mass; it moves in pure translation. The motion is equivalent to a simple pendulum of length $l$.Therefore,the time period is $T = 2\pi \sqrt{\frac{l}{g}}$.

$A$ disc of mass $m$ and radius $R$ is attached to the ceiling with the help of two ropes of length $l$. Find the time period of small oscillations of the disc in the plane of the disc.

Similar Questions

$A$ hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom, the period of oscillation will

$A$ cuboidal piece of wood has dimensions $a, b$ and $c$. Its relative density is $d$. It is floating in a large body of water such that side $a$ is vertical. It is pushed down a bit and released. The time period of $SHM$ executed by it is:

The acceleration due to gravity on the surface of the moon is $1.7 \; m s^{-2}$. What is the time period of a simple pendulum on the surface of the moon if its time period (in $s$) on the surface of the earth is $3.5 \; s$? ($g$ on the surface of the earth is $9.8 \; m s^{-2}$)

The bob of a simple pendulum is hanging vertically down from a fixed identical bob by means of a string of length $l$. If both bobs are charged with a charge $q$ each,what is the time period of the pendulum? (Ignore the radii of the bobs.)

Two pendulums of length $1.21 \,m$ and $1.0 \,m$ start vibrating. At some instant,the two are in the mean position in the same phase. After how many vibrations of the longer pendulum will the two be in phase again?

Vedclass Test Series

Exam Paper Generator

Online Exam Module