Question

Assertion: Light year and wavelength have same dimension.
Reason: Light year represents time while wavelength represents distance.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct and Reason is incorrect.
D. Both Assertion and Reason are incorrect.

Answer 1

In order to solve this question we need a definition of Distance which states that distance is the product of time taken by a particle to go from point ‘A’ to point ‘B’ into the speed through which it travels. It’s a scalar quantity. So to measure distance the fundamental unit is used called a meter denoted by $m$.

Complete answer:
Before we understand what dimension we need to understand about wavelength and light year. So wavelength is defined as distance between consecutive crest and trough of a wave, so it’s a distance which can be measured in units of meter and has a dimension of $[L]$ which means it’s a length quantity.

Light Year is the distance that a light travels in a year with the speed of light which is $3 \times {10^8}m{\sec ^{ - 1}}$. So a light year is too distant and $1$ light year $= 9.461 \times {10^{15}}m$ and this is also a length quantity so its dimension will also be $[L]$. So both quantities are used to express distance but the only difference is that wavelength is a very short distance whereas light year is used to measure astronomical distances which are very large.

So Given assertion is correct which is Light year and wavelength have same dimension
and now the reason is given to us that, Light year represents time while wavelength represents distance which is incorrect because Light year is not a time quantity but a distance quantity so assertion is correct statement but the reason for assertion is incorrect.

Hence, the correct option is C.

Note: It should be remembered that here dimension is defined as the parameter that is used to define a certain physical quantity. Light year and distance both have dimension of distance and generally any physical quantity is represented in dimensions with the other quantities to which a given physical quantity is dependent for example Force on a body is the product of acceleration and mass of the body so dimension of force can be written as $[ML{T^{ - 2}}]$ where $M$ is mass quantity, $L$ is distance quantity and $T$ is time quantity.