At what temperature a ring of certain material of diameter 5.250 cm be heated so that it can befitted on a wooden bangle of diameter 5.260 cm ? Both the diameters have been measured at roomtemperature (27°C ).
Question
At what temperature a ring of certain material of diameter 5.250 cm be heated so that it can befitted on a wooden bangle of diameter 5.260 cm ? Both the diameters have been measured at roomtemperature (27°C ).
Solution
To determine the temperature at which the ring can be fitted onto the wooden bangle, we can use the principle of thermal expansion.
First, we need to calculate the change in diameter of the ring due to the change in temperature. We can use the formula:
ΔD = α * D * ΔT
Where: ΔD is the change in diameter α is the coefficient of linear expansion of the material D is the initial diameter of the ring ΔT is the change in temperature
Since we want to find the temperature at which the ring can be fitted onto the bangle, we need to solve for ΔT. Rearranging the formula, we have:
ΔT = ΔD / (α * D)
Next, we need to calculate the change in diameter of the ring. The change in diameter can be found by subtracting the initial diameter of the ring from the diameter of the wooden bangle:
ΔD = D_bangle - D_ring
Substituting this into the previous equation, we have:
ΔT = (D_bangle - D_ring) / (α * D_ring)
Now, we can plug in the given values. The initial diameter of the ring (D_ring) is 5.250 cm, the diameter of the wooden bangle (D_bangle) is 5.260 cm, and the coefficient of linear expansion (α) depends on the material of the ring.
Once we have calculated ΔT, we can add it to the initial temperature of 27°C to find the temperature at which the ring can be fitted onto the wooden bangle.
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