Home
Class 11
PHYSICS
A semicircular ring has mass m and radiu...

A semicircular ring has mass m and radius R as shown in figure. Let `I_(1),I_(2),I_(3) and I_(4)` be the moments of inertia of the four axes as shown. Axis 1 passes through centre and is perpendicular to plane of ring. Then, match the following columns.

`{:(,"Column-I",,"Column-II"),("(A)",I_(1),"(p)",(mR^(2))/(2)),("(B)",I_(2),"(q)",(3//2)mR^(2)),("(C)",I_(3),"(r)",mR^(2)),("(D)",I_(4),"(s)","Data is insufficient"):}`

Text Solution

Verified by Experts

The correct Answer is:
`(A rarr r,B rarr p,C rarr p,D rarr q)`
Moment of inertia of a ring about an axis perpendicular and passing through the centre of ring is `MR^(2)`. Moment of inertia of a ring about diameter is `MR^(2)//2`. From parallel axes theorem,
`I_(4)=(MR^(2))/(2)+MR^(2)=(3)/(2)MR^(2)`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ROTATION

    DC PANDEY|Exercise (C) Chapter Exercises|39 Videos

  • ROTATION

    DC PANDEY|Exercise (A) Chapter Exercises|83 Videos

  • RAY OPTICS

    DC PANDEY|Exercise Integer type q.|15 Videos

  • ROTATIONAL MECHANICS

    DC PANDEY|Exercise Subjective Questions|2 Videos

Similar Questions

Explore conceptually related problems

A semi-circular ring has mass m and radius R as shown in figure. Let I_(1),I_(2) ,I_(3) " and "I_(4) be the moments of inertia about the four axes as shown . Axis 1 passes through centre and is perpendicular to plane of ring. Then , match the following.

Four rods of equal length l and mass m each forms a square as shown in figure Moment of inertia about three axes 1,2 and 3 are say I_(1),I_(2) and I_(3) . Then, match the following columns {:(,"Column-I",,"Column-II"),("(A)",I_(1),"(p)",(4)/(3)ml^(2)),("(B)",I_(2),"(q)",(2)/(3)ml^(2)),("(C)",I_(3),"(r)",(1)/(2)ml^(2)),(,,"(s)","None"):}

Knowledge Check

  • Let I_(1) and I_(2) be the moment of inertia of a uniform square plate about axes shown in the figure. Then the ratio I_(1):I_(2) is

    A
    `1:(1)/(7)`
    B
    `1:(12)/(7)`
    C
    `1:(7)/(12)`
    D
    `1:7`

  • Consider a semicircular ring with mass m and radius R as shown in figure. Statement-1: The moment of inertia of semi - circular ring about an axis passing through A and perpendicular to plane is 2mR^(2) Statement-2: According to parallel axis theorem: I_(A)=1_(cm)+mR^(2)

    A
    Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
    B
    Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
    C
    Statement-1 is true, statement-2 is false.
    D
    Statement -1 is false, statement -2 is true.

  • Let I_(A) and I_(B) be moments of inertia of a body about two axes A and B respectively. The axis A passes through the centre of mass of the body but B does not

    A
    `I_(A)ltI_(B)`
    B
    If `I_(A)ltI_(B)` the axes are parallel
    C
    If the axes are paralel `I_(A)ltI_(B)`
    D
    if the axes are not parallel the `I_(A)geI_(B)`

    • Similar Questions

    Explore conceptually related problems

    Match the species in Column I with the type of hybrid orbitals in Column II. {:(,"Column I",,"Column II"),((i),BF_(3),(a),sp^(3)d),((ii),H_(2)O,(b),sp^(2)),((iii),PCl_(5),(c),sp^(3)d^(2)),((iv),SF_(6),(d),sp^(3)):}

    Calculate the values of currents · I_(1)I_(2)I_(3) and I_(4) Is and loin the section of networks shown in the figure

    Let I_(A) and I_(B) be moments of inertia of a body about two axes A and B respectively. The axis A passes through the centre of mass of the body but B does not

    Which option is correct if I_(1) , I _(2) and I_(3) are moments of inertia of solid sphere, hollow sphere and a ring of same mass and radius,

    A ring and a thin hollow cylinder have the same mass and radius. If I_(r ) and I_(s) represent their moment of inertia about their axes, then

    Home
    Profile