Question

Two uniform brass rods A and B of length land 2l and radii 2r and r respectively are heated to the same temperature. The ratio of the increase in the volume ofB to that of A is ____________.

Options

• 1 : 1

• 1 : 2

• 2 : 1

• 1 : 4

Answer 1

Two uniform brass rods A and B of length land 2l and radii 2r and r respectively are heated to the same temperature. The ratio of the increase in the volume ofB to that of A is 1 : 2.

Explanation:

Let the original temperature be 0 °C;

Volume of `A = V_1 =l xx pi(2r)^2`;

After heating volume of A will become,

`V'_1 = V_1(1+ gammaDeltaT)`

`(V'_1 -  V_1)/V_1 = gammaDeltaT Rightarrow V'_1 - V_1 prop V_1`

Similarly for rod B,

`(V'_2 -  V_2)/V_2 = gammaDeltaT Rightarrow V'_2 - V_2 prop V_2`

`therefore (Delta V_2)/(Delta V_1)= (2lr^2)/(l(2r)^2)= 1/2`