question_answer

The speed of light in air is \[3.00\times {{10}^{8}}m/s\]. The distance travelled by light in one year \[\left( \text{i}.\text{e}.,\text{ 365 days }=\text{3}\text{.154}\times \text{1}{{0}^{\text{7}}}\text{ s} \right)\] is known as one light year. A student calculates one light year \[=9.462\times {{10}^{15}}m\]          Do you agree with the student? If not, what should be the correct value of one light year?

Answer:

                We know that, one light year = speed of light x time (one year)                                                                          \[=\left( \text{3}.00\times \text{1}{{0}^{\text{8}}} \right)\times \left( \text{3}\text{.154}\times \text{1}{{0}^{\text{7}}} \right)=\text{9}\text{.462}\times \text{1}{{0}^{\text{15}}}\text{ m}\] As per rule, when two physical quantities are multiplied, the number of significant figures in the result cannot be greater than the least number of significant figures in any of the two quantities. We do not agree with the student. The product is, therefore, rounded off to contain three significant figures. We may write:    one light year =\[\text{9}\text{.46}\times \text{1}{{0}^{\text{15 }}}\text{m}\].