Home
Class 11
PHYSICS
A weightless rigid rod with a small iron...


A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible string of length `20cm`, fixed at its midpoint. The bob is displaced slightly perpenducular to the plane of the rod and string. Find period of small oscillations of the system in the form `(piX)/(10)s` and fill the value of X.

Text Solution

Verified by Experts


The bob will exicute SHM about the stationary axis passing through AB. If its effective length is `l` then `T=2pisqrt((l')/(g'))`
`l'=(l)/(sintheta)=sqrt2l`
[because `theta=45^@]`
`g^(`)=gcostheta=(g)/(sqrt2_)`
`T=2pisqrt((2l)/(g))=2pisqrt((2xx0.2)/(10))=(2pi)/(5)s`
`X=4`
Promotional Banner

Topper's Solved these Questions

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS|Exercise Subjective type|2 Videos

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS|Exercise Multiple Correct Answer Type|6 Videos

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS|Exercise Comprehension|33 Videos

  • KINETIC THEORY OF GASES AND FIRST LAW OF THERMODYNAMICS

    CENGAGE PHYSICS|Exercise Interger|11 Videos

  • MISCELLANEOUS KINEMATICS

    CENGAGE PHYSICS|Exercise Interger type|3 Videos

Similar Questions

Explore conceptually related problems

A weightless rigid rod with a load at the end is hinged at point A to the wall so that it can rotate in all directions (Fig). The rod is kept in the horizontal position by a vertical inextensible thread of length 1, fixed at its midpoint. The load receives a momentum in the direction perpendicular to the plane of the figure. Determine the period T of small oscillations of the system.

There is a rod of length l and mass m . It is hinged at one end to the ceiling. The period of small oscillation is

A steel rod of length L, density d and cross-sectional area A, is hinged at one end so that it can rotate freely in a vertical plane. The rod is released from a horizontal position. When it becomes vertical, the stress at its midpoint is

A uniform rod AB hinged about a fixed point P is initially vertical. A rod is released from vertical position. When rod is in horizontal position: The acceleration of end B of the rod is

A uniform rod AB of length L and and weight Mg is hinged at one end A. The rod is kept in the horizontal position by a massless string. If the string is cut, then the angular acceleration of the rod will be ["M.I. of the rod about A is "(ML^(2))/(3)]

A uniform rod of mass m and length L is hinged at one of its end with the ceiling and another end of the rod is attached with a thread which is attached with the horizontal ceiling at point P. If one end of the rod is slightly displaced horizontally and perpendicular to the rod and released. If the time period of small oscillation is 2pisqrt((2lsintheta)/(xg)) . Find x.

A uniform rod AB hinged about a fixed point P is initially vertical. A rod is released from vertical position. When rod is in horizontal position: The reaction at hinge P is

A uniform rod AB hinged about a fixed point P is initially vertical. A rod is released from vertical position. When rod is in horizontal position: The acceleration of the centre of mass of the rod is

Two light strings, each of length l are fixed at points A and B on a fixed horizontal and xy A small are making angle 45^(@) with the bob if the bob is displeced normal to the plane of the string and released then period of the resulting small oscillation will be