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Byju's Answer

Standard IX

Physics

Thermal Expansion

Two rods of l...

Question

Two rods of length $L_{2}$ and coefficient of linear expansion $α_{2}$ are connected freely to a third rod of length $L_{1}$ of coefficient of linear expansion $α_{1}$ to form an isosceles triangle. The arrangement is supported on the knife edge at the midpoint of $L_{1}$ which is horizontal. The apex of the isosceles triangle is to remain at a constant distant from the knife edge if

\frac{L_{1}}{L_{2}} = \frac{α_{2}}{α_{1}}

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\frac{L_{1}}{L_{2}} = \sqrt{\frac{α_{2}}{α_{1}}}

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\frac{L_{1}}{L_{2}} = 2 \frac{α_{2}}{α_{1}}

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\frac{L_{1}}{L_{2}} = 2 \sqrt{\frac{α_{2}}{α_{1}}}

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Solution

The correct option is D $\frac{L_{1}}{L_{2}} = 2 \sqrt{\frac{α_{2}}{α_{1}}}$

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Similar questions

Q. Two rods of length

L_{2}

and coefficient of linear expansion

α_{2}

are connected freely to a third rod of length

L_{1}

of coefficient of linear expansion

α_{1}

to form an isosceles triangle. The arrangement is supported on the knife edge at the midpoint of

L_{1}

which is horizontal. The apex of the isosceles triangle is to remain at a constant distance from the knife edge if

Q. Two rods of length

L_{2}

and coefficient of linear expansion

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are connected freely to a third rod of length

L_{1}

of coefficient of linear expansion

α_{1}

to form an isosceles triangle. The arrangement is supported on the knife edge at the midpoint of rod of length

L_{1},

which is horizontal. The apex of the isosceles triangle remains at a constant distance from the knife edge, if

\frac{L_{1}}{L_{2}} = n {(\frac{α_{2}}{α_{1}})}^{\frac{1}{2}}

. Then value of

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Q. Two rods of length

L_{2}

and coefficient of linear expansion

α_{2}

are connected freely to a third rod of length

L_{1}

of coefficient of linear expansion

α_{1}

to form an isosceles triangle. The arrangement is supported on the knife edge at the midpoint of rod of length

L_{1},

which is horizontal. The apex of the isosceles triangle remains at a constant distance from the knife edge, if

\frac{L_{1}}{L_{2}} = n {(\frac{α_{2}}{α_{1}})}^{\frac{1}{2}}

. Then value of

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L_{2}

and coefficient of linear expansion

α_{2}

each are connected freely to a third rod of length

L_{1}

and coefficient of expansion

α_{1}

to form an isosceles triangle. The arrangement is supported on a knife-edge at the midpoint of

L_{1}

which is horizontal. What relation must exist between

L_{1}

and

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Q. Two rods each of length

L_{2}

and coefficient of linear expansion

α_{2}

each are connected freely to a third rod of length

L_{1}

and coefficient of expansion

α_{1}

to form an isosceles triangle. The arrangement is supported on a knife-edge at the midpoint of

L_{1}

which is horizontal. What relation must exist between

L_{1}

and

L_{2}

so that the apex of the isosceles triangle is to remain at a constant height from the knife edge as the temperature changes.

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The correct option is D L1L2=2√α2α1

The correct option is D $\frac{L_{1}}{L_{2}} = 2 \sqrt{\frac{α_{2}}{α_{1}}}$