Question

A metal sphere 10.01 cm in diameter is placed on a brass ring of internal diameter 10 cm and at the same temperature of 12° C. The temperature up to which they should be heated together so that the metal sphere just passes through the ring is `[alpha_"metal"= 12 xx 10^-6//°"C" and alpha_"brass" =18 xx 10^-6//°"C"]` ____________.

Options

• 167° C

• 179° C

• 191° C

• 197° C

Answer 1

A metal sphere 10.01 cm in diameter is placed on a brass ring of internal diameter 10 cm and at the same temperature of 12° C. The temperature up to which they should be heated together so that the metal sphere just passes through the ring is 179° C.

Explanation:

Diameter of sphere = Diameter of ring

`10.01 [1 + 12 xx 10^-6 ("t"_2 - 12)]`

`= 10[1 + 18 xx 10^-6 ("t"_2 - 12)]`

`1.001 + 1.001 xx 12 xx 10^-6 ("t"_2 - 12) = 1 + 18 xx 10^-6 ("t"_2 - 12)`

`1.001 - 1 = 18 xx 10^-6 ("t"_2 - 12) - 1.001 xx 12 xx 10^-6 ("t"_2 - 12)`

`10^-3 = ("t"_2 - 12) xx 10^-6 [18 - 12.012]`

`therefore "t"_2 - 12 = 10^-3/5.988 xx 10^-6`

`therefore "t"_2 approx 179 °"C"`