Question

The length of a right circular cylinder increases due to heating by \[0.1\% \]. It base will increase by
(A) \[0.1\% \]
(B) \[0.2\% \]
(C) \[0.01\% \]
(D) \[\left( {22 \times 0.01} \right)/7\% \]

Answer 1

Hint: In this question length of the circular cylinder increases due to heating. For calculating the increase in base, we will calculate the value of change in area.
Also remember that the volume of the cylinder is \[\pi {r^2}h\], here r is the radius of the cylinder, h is the height of the cylinder.

Complete answer:
As we know that length will change on heating. When the length is increased then it will also affect the radius of the cylinder. Then the value of area or change in area will be increased.
According to this question, length is increased by \[0.1\% \]on heating then radius will also increase by \[0.1\% \]. If we calculate the change in area then it will be
\[ \Rightarrow \delta A = 2\delta r\]
Here \[\delta A\] is the change in area and \[\delta r\] is the change in radius,
Now substitute the value of the change in area and the change in radius,
We get- \[\delta A\]=\[2 \times \] \[0.1\% \]\[ = 0.2\% \]

So, the correct answer is “Option B”.

Note:
When there is increase in length due to increase in temperature then such expansion is known as linear expansion and this change in length is directly proportional to the length of the rod, change in temperature and the coefficient of expansion/ nature of material of rod. This increase in the length of rod when heating does not depend on whether the rod is hollow or solid.