To determine the duration of the \(E_2\) dose at 50 cm, we need to understand the inverse square law, which applies to the intensity of light. The law states that intensity is inversely proportional to the square of the distance from the source. Thus, if the distance is halved, the intensity increases by a factor of four.
- The given \(E_1\) dose duration is 1 minute (60 seconds) at a distance of 100 cm. Therefore, this dose can be represented as:
\(I_1 = \frac{Dose}{(100)^2}\)
- We need to find the duration \(t_2\) for the \(E_2\) dose at 50 cm distance:
\(I_2 = \frac{Dose}{(50)^2}\)
- According to the inverse square law:
\(I_1 \times t_1 = I_2 \times t_2\)
- Substitute the values and solve for \(t_2\):
\(\frac{1}{(100)^2} \times 60 = \frac{1}{(50)^2} \times t_2\)
- Simplify the equation:
\(\frac{60}{10000} = \frac{t_2}{2500}\)
- Multiply both sides by 2500 to solve for \(t_2\):
\(t_2 = \frac{60 \times 2500}{10000}\)
- Simplify:
\(t_2 = 15 \times 2.5 = 37.5\) seconds
- Therefore, the duration of the \(E_2\) dose at 50 cm is 37.5 seconds.
Thus, the correct answer is 37.5 seconds.
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Important Questions from Mixed Topic (CUET PG)
- Kalpsutra, the illustrated canonical text is from:-
- The Harappan city almost exclusively devoted to craft production was-:
- Mohandas Karamchand Gandhi launched quit India movement after the failure of:-
- The "Objectives Resolution" was introduced in constituent assembly by:-
- Who among the following was not a member of the constituent assembly:-
