कमानी स्थिरांक \(100\; N / m\) की किसी कमानीदार बन्दूक में द्रव्यमान \(100\; g\) की कोई छोटी गेंद \('B'\) इसकी बैरल में (आरेख देखिए) कमानी को \(0.05\; m\) संपीडित करके रखी है। धरती पर दूरी \(d\) पर किसी बॉक्स को रखा जाना चाहिए ताकि यह गेंद उस बॉक्स में गिरे। यदि गेंद धरती से \(2 \;m\) ऊँचाई पर बन्दूक से क्षैतिजत : निकलती है तो \('d'\) का मान \(\dots\;m\) होगा। \(\left( g =10\; m / s ^{2}\right)\)

A \(51\)
B \(212\)
C \(1\)
D \(9\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(1\)

Step-by-step Solution

Detailed explanation

\(\frac{1}{2} k x^{2}=\frac{1}{2} m v^{2}\) \(k x^{2}=m v^{2}\) \(V=x \sqrt{\frac{k}{m}}=0.05 \sqrt{\frac{100}{1}}=0.05 \times 10 \sqrt{10}\) \(v=0.5 \sqrt{10}\) From \(h=\frac{1}{2} g t^{2}\) \(t=\sqrt{\frac{2 h}{g}}=\sqrt{\frac{2 \times 2}{10}}=\frac{2}{\sqrt{10}}\)…

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.

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