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Standard XII

Physics

Thermal Expansion

When a rod is...

Question

When a rod is heated from $25^{\circ} C$ to $75^{\circ} C,$ it expands by $1 m m .$ When a rod of same material but with 4 times the length is heated from $25^{\circ} C$ to $50^{\circ} C .$ The increase in length is :

1 m m

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1.5 m m

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1.6 m m

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2 m m

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Solution

The correct option is D $2 m m$
In the first case, $d t = 50$ , $d l = 1$ mm $= 0.001$ m, $l = l$
So, $α = \frac{d l}{l X d t}$ $=$ $\frac{0.001}{50 l}$

In the second case,
$d l = α \times 4 l \times d t$ (putting the value of $α$ )
$d l = 0.002$ m $= 2$ mm

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When a rod is heated from 25∘ C to 75∘ C, it expands by 1 mm. When a rod of same material but with 4 times the length is heated from 25∘ C to 50∘ C. The increase in length is :

The correct option is D 2mmIn the first case, dt=50, dl=1mm =0.001m, l=lSo, α=dllXdt = 0.00150lIn the second case,dl=α×4l×dt (putting the value of α)dl=0.002m =2mm

When a rod is heated from $25^{\circ} C$ to $75^{\circ} C,$ it expands by $1 m m .$ When a rod of same material but with 4 times the length is heated from $25^{\circ} C$ to $50^{\circ} C .$ The increase in length is :

The correct option is D $2 m m$
In the first case, $d t = 50$ , $d l = 1$ mm $= 0.001$ m, $l = l$
So, $α = \frac{d l}{l X d t}$ $=$ $\frac{0.001}{50 l}$

In the second case,
$d l = α \times 4 l \times d t$ (putting the value of $α$ )
$d l = 0.002$ m $= 2$ mm