दो प्रक्षेप्य समान प्रारंभिक वेगों से क्षैतिज के सापेक्ष \(15^\circ\) और \(30^\circ\) के कोण पर प्रक्षेपित किए जाते हैं। उनकी परासों का अनुपात \(1:x\) है। \(x\) का मान है:

A \(\sqrt{2}\)
B \(\sqrt{3}\)
C \(2\sqrt{3}\)
D \(\dfrac{1}{\sqrt{2}}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\sqrt{3}\)

Step-by-step Solution

Detailed explanation

किसी प्रक्षेप्य की क्षैतिज परास का सूत्र \(R = \dfrac{u^2 \sin(2\theta)}{g}\) द्वारा दिया जाता है। पहले प्रक्षेप्य के लिए, प्रक्षेप कोण \(\theta_1 = 15^\circ\) है। \(R_1 = \dfrac{u^2 \sin(2 \times 15^\circ)}{g} = \dfrac{u^2 \sin(30^\circ)}{g} = \dfrac{u^2}{2g}\) दूसरे प्रक्षेप्य…

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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