একটি বল P অপর একটি বল P-এর সঙ্গে 20° কোণ উৎপন্ন করে। বলছয়ের লম্বি হবে
A$P \cos 20^\circ$
B$2P \cos 20^\circ$
C$2P \cos 10^\circ$
D$P \cos 10^\circ$
Answer & Solution
Correct answer: C. $2P \cos 10^\circ$
দুটি সমান বলের মান $P$ এবং তাদের মধ্যবর্তী কোণ $20^\circ$। সমান দুটি বলের লব্ধির মান হয়
$$R=\sqrt{P^2+P^2+2P^2\cos20^\circ}$$
$$R=\sqrt{2P^2(1+\cos20^\circ)}$$
এখন, $1+\cos20^\circ=2\cos^2 10^\circ$ ব্যবহার করলে
$$R=\sqrt{4P^2\cos^2 10^\circ}$$
$$R=2P\cos10^\circ$$
অতএব সঠিক উত্তর $C$।
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