A Harrison's grid iron pendulum consists of $7$ iron rods and $6$ brass rod. If length of each brass rod is $20 c m$ . What is the length of each iron rod
$[\propto i r o n = 120 \times 10^{- 6} /^{\circ} C]$
$[\propto b r a s s = 20 \times 10^{- 6} /^{\circ} C]$

36 c m

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75 c m

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120 c m

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25 c m

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Solution

The correct option is D $25 c m$
On comparison of linear expansion consider brass and iron rods on one side of central iron.
Effective length of $4$ iron rods $= 4 \times l = 4 l$
Effective length of $3$ brass rods $= 3 \times 20 = 60 c m$ .
Increase in length of iron rods $=$ Increase in length of brass rods.
$4 l \times 12 \times 10^{- 6} \times t = 60 \times 20 \times 10^{- 6} \times t$
$l = \frac{60 \times 20 \times 10^{- 6}}{4 \times 12 \times 10^{- 6}} = 25 c m$

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Similar questions

Q. In a grid iron pendulum, there are 3 iron rods and 4 brass rods, Length of each brass rod is 50 cm.

α

of iron is

12 \times 10^{- 6} /^{\circ} C

and

α

of Brass is

18 \times 10^{- 6} /^{\circ} C

. Length of each iron rod is

Q. Assertion(A): In a grid pendulum, there are 3 iron rods and 4 brass rods. Length of each brass rod is

50 c m

α

of iron is

12 \times 10^{- 6} /^{o} C

and

α

of brass is

18 \times 10^{- 6} /^{o} C

. Length of each iron rod is

50 c m .

Reason(R): for grid iron pendulum

n_{1} l_{1} α_{1} + n_{2} l_{2} α_{2} = 1

An iron rod and another of brass, both at $27^{\circ} C$ differ in length by $10^{- 3} m$ . The coefficient of linear expansion for iron is $1.1 \times 10^{- 5}$ $/^{\circ} C$ and for brass is $1.9 \times 10 - 5$ $/^{\circ} C$ . The temperature at which both these rods will have the same length is