Home
Class 12
PHYSICS
A rod of uniform cross-section of mass M...

A rod of uniform cross-section of mass `M` and length `L` is hinged about an end to swing freely in a vertical plane. However, its density is non uniform and varies linearly from hinged end to the free end doubling its value. The moment of inertia of the rod, about the rotation axis passing through the hinge point

A

`(2ML^(2))/(9)`

B

`(3ML^(2))/(16)`

C

`(7 ML^(2))/(18)`

D

None

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DAILY PRACTICE PROBLEM

    RESONANCE|Exercise DPP No.68|9 Videos

  • DAILY PRACTICE PROBLEM

    RESONANCE|Exercise DPP No.69|20 Videos

  • DAILY PRACTICE PROBLEM

    RESONANCE|Exercise DPP No.66|20 Videos

  • CURRENT ELECTRICITY

    RESONANCE|Exercise High Level Problems (HIP)|21 Videos

  • ELECTRO MAGNETIC WAVES

    RESONANCE|Exercise Exercise 3|27 Videos

Similar Questions

Explore conceptually related problems

A thin uniform wire of mass m and length l is bent into to shape of a semicircle. The moment of inertia of that wire about an axis passing through its free ends is

A uniform rod of mass M and length L is hinged at its end. The rod is released from its vertical position by slightly pushing it. What is the reaction at the hinge when the rod becomes horizontal, again vertical.

Knowledge Check

  • The moment of inertia of a thin uniform rod of mass M and length L about an axis perpendicular to the rod, through its centre is I . The moment of inertia of the rod about an axis perpendicular to rod through its end point is

    A
    `I/4`
    B
    `I/2`
    C
    `2I`
    D
    `4I`

  • Moment of inertia of a thin uniform rod about an axis passing through one end perpendicular to its length is I . Then moment of inertia the same rod about the central axis perpendicular to its plane is

    A
    `I//4`
    B
    2I
    C
    4I
    D
    3 I

  • The moment of inertia of a thin uniform rod of mass M and length l about an axis perpendicular to the rod through its centre is I. The moment of inertia of the rod through its end point is

    A
    `(I)/(4)`
    B
    `(I)/(2)`
    C
    `2I`
    D
    `4I`

    • Similar Questions

    Explore conceptually related problems

    The moment of inertia of a thin uniform rod about an axis passing through its centre and perpendicular to its length is I_(0) . What is the moment of inertia of the rod about an axis passing through one end and perpendicular to the rod ?

    A uniform rod of mass M & length L is hinged about its one end as shown. Initially it is held vartical and then allowed to rotate, the angular velocity of rod when it makes an angle of 37^(@) with the vertical is

    Calculate the moment of inertia of a rod of mass M, and length l about an axis perpendicular to it passing through one of its ends.

    In the figure a uniform rod of mass 'm' and length 'l' is hinged at one end and the other end is connected to a light vertical of spring constant 'k' as shown in figure. The spring has extension such that rod is equilibrium when it is horizontal . The rod rotate about horizontal axis passing through end 'B' . Neglecting friction at the hinge find (a) extension in the spring (b) the force on the rod due to hinge.

    A thin rod of mass m and length l is hinged at the lower end to a level floor and stands vertically. Then its upper end will strike the floor with a velocity given by:

    Home
    Profile