The coefficient of linear expansion of brass and steel are α 1 and α 2 . If we take a brass rod of length l 1 and steel rod of length l 2 a t 0 ∘ C , their difference in length ( l 2 − l 1 ) will remain the same at a temperature if Options: A . &nbspα1l2=α2l1 B . &nbspα1l22=α2l21 C . &nbspα21l1=α22l2 D . &nbspα1l1=α2l2

Answer: Option D : D d ) L 2 = l 2 ( l + α 2 △ θ ) and L 1 = l 1 ( l + α 1 △ θ ) ⇒ ( L 2 − L 1 ) = ( l 2 − l 1 ) + △ θ ( l 2 α 2 − l 1 α 1 ) Now ( L 2 − L 1 ) = ( l 2 − l 1 ) so, l 2 α 2 − l 1 α 1 = 0

The coefficient of linear expansion of brass and steel are α1 a

Question

The coefficient of linear expansion of brass and steel are

α_{1}

and

α_{2}

. If we take a brass rod of length

l_{1}

and steel rod of length

l_{2} a t 0^{\circ} C,

their difference in length

(l_{2} - l_{1})

will remain the same at a temperature if

Options:

A . α1l2=α2l1

B . α1l22=α2l21

C . α21l1=α22l2

D . α1l1=α2l2

Answer: Option D
:
D

d) L_{2} = l_{2} (l + α_{2} △ θ)

and

L_{1} = l_{1} (l + α_{1} △ θ)

\Rightarrow (L_{2} - L_{1}) = (l_{2} - l_{1}) + △ θ (l_{2} α_{2} - l_{1} α_{1})

Now

(L_{2} - L 1) = (l_{2} - l_{1})

so,

l_{2} α_{2} - l_{1} α_{1} = 0

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