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A homogeneous plate PQRST is as shown in...

A homogeneous plate `PQRST` is as shown in figure. The centre of mass of plate lies at midpoint `A` of segment `QT`. Then the ratio of `(b)/(a)` is `(PQ=PT=b,QR=RS=a)`

A

`(13)/(4)`

B

`(13)/(2)`

C

`sqrt((13)/(2))`

D

`sqrt((13)/(4))`

Text Solution

Verified by Experts

The correct Answer is:
D
If centre of mass is at `A`
`a^(2)sigma(a)/(2)=sigma(1)/(2)ab sin theta(1)/(3) b sin theta`
or `(b)/(a)=sqrt((13)/(4))`
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Knowledge Check

  • A homogeneous plate PQRST is as shown in figure. The centre of mass of plate lies at midpoint A if segment QT . Then the ratio of (b)/(a) is (PQ = PT = b , QR = RS = ST = a) .

    A
    `(13)/(4)`
    B
    `(13)/(2)`
    C
    `sqrt((13)/(2))`
    D
    `sqrt((13)/(4))`

  • Two uniform plates of the same thickness and area but of different materials, one shaped like an isosceles triangle and the other shaped like a rectangle are joined together to form a composite body as shown in the figure. If the centre of mass of the composite body is located at the midpoint of their common side, the ratio between masses of the triangle to that of the rectangle is -

    A
    `1 : 1`
    B
    `4 : 3`
    C
    `3 : 4`
    D
    `2 : 1`

  • A hole of radius R/2 is cut from a thin circular plate of raduis R as shown in the figure. If the mass of the remaining plate is M, then find moment of inertia of the plate about an axis through O perpendicular to plane

    A
    `13/25 MR^(2)`
    B
    `13/24 MR^(2)`
    C
    `11/24 MR^(2)`
    D
    `11/25 MR^(2)`

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