Question

On a cold day, a metal measuring tape graduated in millimetres is used to measure the distance between two fence posts. The measuring tape reads 3.00 m.
On a much hotter day, the metal measuring tape is used to measure the length of the same
distance again. The metal measuring tape has a higher temperature than the ground. The temperature of the ground remains constant.
Which statement is correct?
(A). The metal measuring tape reads less than 3.00 m because the graduations are closer together.
(B). The measuring tape reads less than 3.00m because the graduations are further apart
(C). The measuring tape reads more than 3.00 m because graduations are closer together
(D. The measuring tape reads more than 3.00 m because the graduations are further apart

Answer 1

- Hint: Find out the dependence of length of metal with increasing or decreasing temperature. The increase in length of metal with increase in temperature is called the linear expansion. With the help of this concept answer the question.

Complete step-by-step solution -
Length of a metal depends on the temperature of the metal. With increase in temperature the length of the metal will also increase and with decrease in temperature the length of the metal will also decrease. The change in length of the metal depends on the initial length of the metal and on the change in temperature.
This is called the linear expansion. Linear expansion can be mathematically expressed as,
$\Delta L=\alpha {{L}_{0}}\Delta T$
Here, $\Delta L$ is the change in length of the metal, $\alpha$ is the coefficient of linear expansion, ${{L}_{0}}$ is the initial length of the metal and $\Delta T$ is the change in temperature.
Since metal expands with increase in temperature, on hotter days the length of the measuring tape will increase. So, the graduations will be farther apart than they are on a colder day. So, we can say that the tape will measure the same distance as less in colder days and larger in hotter days.
So, we can say that the measuring tape reads less than 3.00m because the graduations are further apart.
The correct option is (B).

Note: We have three types of thermal expansions – linear expansion, superficial expansion and cubical expansion. The linear expansion gives expansion of length, superficial expansion gives expansion of area and cubical expansion gives expansion of volume of metal.