0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

# A thin uniform metallic triangular sheet of mass M has sides AB=BC=L. Its moment of inertia about the axis AC lying in the plane of the sheet is:ML212ML232ML23ML26

A
ML26
B
ML23
C
ML212
D
2ML23
Solution
Verified by Toppr

#### The given triangular sheet has an area equal to half of a square sheet having same side length as the length of the base of the triangle.Let MI of the triangular sheet about AC be I.I is half of the MI of the square plate about an axis passing through the centre O and being in the plane of the plate.Let the MI of the square about an axis XY be IXY.Due to symmetryIAB=ICD AND IPQ=IRSLet Isquare be the MI a bout an axis passing through the centre of the square and perpendicular to the plane of the square plate.Then using Perpendicular Axis TheoremIsquare=IAB+ICD=IPQ+IRS∴Isquare=2IAB=IPQBut, IAB=2I∴I=12IAB=12∗(12ML26) ....(1) where M is the mass of the square plate.But the triangular sheet has half the mass of the square plate. Writing I in terms of the mass of the plate.∴I=M2∗L2/12=112MtriangleL2

1
Similar Questions
Q1
A thin uniform metallic triangular sheet of mass M has sides AB=BC=L. Its moment of inertia about the axis AC lying in the plane of the sheet is:
View Solution
Q2

In a metallic triangular sheet ABC. AB = BC = L. If M is mass of sheet, what is the moment of inertia about AC

View Solution
Q3

Moment of inertia of a thin rod of mass M and length L about an axis passing through centre is ML​​​​​2/12. Its moment of inertia about a parallel axis at a distance of L/4 from the axis is given by?

A. ML2/48

B. ML3/48

C. ML2/12

D. 7ML2/48

View Solution
Q4
The moment of inertia of a uniform thin rod of mass m and length l about the axis PQ and RS passing through center of rod C and in the plane of the rod are IPQ and IRS respectively. Then IPQ+IRS is equal to

View Solution
Q5
The moment of inertia of a uniform rod of length 2l and mass m about an axis xx passing through its centre and inclined at an angle α is

View Solution