વરસાદના ટીપાનું દળ \(3.0\times10^{-5}\, kg\) અને સરેરાશ ટર્મિનલ વેગ \(9\, m/s\) છે. આ ટીપાં દ્વારા પ્રતિ દર વર્ષે \(100\, cm\) વરસાદ મેળવતી \(1\,cm^2\) સપાટી પર કેટલી ઉર્જા મેળવાશે?

A \(3.5\times10^5\, J\)
B \(4.05\times10^4\, J\)
C \(3.0\times10^5\, J\)
D \(9.0\times10^4\, J\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(4.05\times10^4\, J\)

Step-by-step Solution

Detailed explanation

Total volume of rain drops, recrived \(100\,cm\) in a year by area \(1\,m^2\) \( = 1{m^2} \times \frac{{100}}{{100}}m = 1\,{m^3}\) As we know, density of water, \(d = {10^3}\,kg/{m^3}\) Therefore, mass of this volume of water, \(M = d \times v = {10^3} \times 1 = {10^3}\,kg\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

\((4 \hat{ i }+3 \hat{ j }-\hat{ k }) m \cdot\) બિંદુ પર લાગતું બળ \(\overrightarrow{ F }=(\hat{ i }+2 \hat{ j }+3 \hat{ k }) N\) છે, \((\hat{i}+2 \hat{j}+\hat{k}) m\) બિંદુને અનુલક્ષીને ટોર્ક \(\sqrt{ x } N - m\) હોય તો \(x = ........\)

JEE Mains 2020 Medium

Match List\(-I\) with List\(-II.\)

List\(-I\)	List\(-II\)
\((a)\) ચુંબકીય પ્રેરણ	\((i)\) \({ML}^{2} {T}^{-2} {A}^{-1}\)
\((b)\) ચુંબકીય ફ્લક્સ	\((ii)\) \({M}^{0} {L}^{-1} {A}\)
\((c)\) ચુંબકીય પરમીએબીલીટી	\((iii)\) \({MT}^{-2} {A}^{-1}\)
\((d)\) મેગ્નેટાઇઝેશન	\((iv)\) \({MLT}^{-2} {A}^{-2}\)

આપેલ વિકલ્પો માંથી સાચો વિકલ્પ પસંદ કરો.

JEE Mains 2021 Medium

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