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The ABC is a triangular plate of uniform...

The ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. `I_(AB) , I_(BC)` and `l_(CA)` are the moments of inertia of the plate about AB, BC and CA respectively. Which one of the following relation is correct?

A

`I_(AB)+I_(BC)=I_(CA)`

B

`I_(CA)` is maximum

C

`I_(AB)gtI_(BC)`

D

`I_(BC)gtI_(AB)`

Text Solution

Verified by Experts

The correct Answer is:
D
The intersection of medians is the centre of mass of the triangle. Since the distances of centre of mass from the sides is related as `x_(BC)gt x_(AB) gt x_(AC)`·

Therefore `I_(BC)gtI_(AB)gtI_(AC)` or `I_(BC)gtI_(AB)`
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Knowledge Check

  • ABC is a triangular plate of uniform A thickness. The sides are in the ratio shown in the figure. I_(AB), I_(BC), I_(CA) are the moments of inertia of the plated about AB, BC and CA respectively. Which one of the following relation is correct?

    A
    `I_(CA)` is maximum
    B
    `I_(AB)gtI_(BC)`
    C
    `I_(BC)gtI_(AB)`
    D
    `I_(AB)+I_(BC)=I_(CA)`

  • ABC is a right angled triangular plate of uniform thickness. The sides are such that AB gt BC as shown in figure. I_(1),I_(2) and I_(3) are moments of inertia about AB,BC and AC respectively. Then, which of the following relation is correct ?

    A
    `I_(1)=I_(2)=I_(3)`
    B
    `I_(2) gt I_(1) gt I_(3)`
    C
    `I_(3) lt I_(2) lt I_(1)`
    D
    `I_(2) gt I_(1) gt I_(2)`

  • ABC is a right angled triangular plate of uniform thickness. The sides are such that AB gt BC as shown in figure. I_(1), I_(2), I_(3) are moments of inertia about AB, BC and AC respectively. Then which of the following relations is correct?

    A
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    B
    `I_(2) gt I_(1) gt I_(3)`
    C
    `I_(3) lt I_(2) lt I_(1)`
    D
    `I_(3) gt I_(1) gt I_(2)`

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