SATHEE: Properties Of Solids And Liquids Question 116

Properties Of Solids And Liquids Question 116

Question: Three rods of equal length l are joined to form an equilateral triangle PQR. O is the mid point of PQ. Distance OR remains same for small change in temperature. Coefficient of linear expansion for PR and RQ is same i.e. $α_{2}$ but that for PQ is $α_{1}$ . Then

Options:

A) $α_{2} = 3 α_{1}$

B) $α_{2} = 4 α_{1}$

C) $α_{1} = 3 α_{2}$

D) $α_{1} = 4 α_{2}$

Show Answer

Answer:

Correct Answer: D

Solution:

${(O R)}^{2} = {(P R)}^{2} - {(P O)}^{2} = l^{2} - {(\frac{l}{2})}^{2}$

$= {[l (1 + α_{2} t)]}^{2} - {[\frac{l}{2} (1 + α_{1} t)]}^{2}$

$l^{2} - \frac{l^{2}}{4} = l^{2} (1 + α_{2}^{2} t^{2} + 2 α_{2} t) - \frac{l^{2}}{4} (1 + α_{1}^{2} t^{2} + 2 α_{1} t)$

Neglecting $α_{2}^{2} t^{2}$

and $α_{1}^{2} t^{2}$

$0 = l^{2} (2 α_{2} t) - \frac{l^{2}}{4} (2 α_{1} t) \Rightarrow 2 α_{2} = \frac{2 α_{1}}{4} \Rightarrow; α_{1} = 4 α_{2}$

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Properties Of Solids And Liquids Question 116

Question: Three rods of equal length l are joined to form an equilateral triangle PQR. O is the mid point of PQ. Distance OR remains same for small change in temperature. Coefficient of linear expansion for PR and RQ is same i.e. α2 but that for PQ is α1 . Then

Options:

Answer:

Solution:

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Question: Three rods of equal length l are joined to form an equilateral triangle PQR. O is the mid point of PQ. Distance OR remains same for small change in temperature. Coefficient of linear expansion for PR and RQ is same i.e. $α_{2}$ but that for PQ is $α_{1}$ . Then