ठोस शाफ्ट के समान अनुप्रस्थ-काट क्षेत्र का एक खोखला शाफ्ट __________संचरित करेगा

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  1. समान बलाघूर्ण
  2. कम बलाघूर्ण
  3. अधिक बलाघूर्ण
  4. बाहरी व्यास के आधार पर कम या अधिक

Answer (Detailed Solution Below)

Option 3 : अधिक बलाघूर्ण
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Detailed Solution

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व्याख्या:

चूँकि अनुप्रस्थ-काट का क्षेत्र समान है,

\(\frac{\pi }{4}\left( {d_1^2 - d_2^2} \right) = \frac{\pi }{4}d_s^2\)

\(\therefore d_1^2 - d_2^2 = d_s^2\)

\(\frac{τ }{r} = \frac{T}{J} = \frac{{G\theta }}{L}\)

\(T=\frac{τJ }{r}\)

अब बलाघूर्ण ∝ ध्रुवीय आघूर्ण

\(\therefore \frac{{{T_h}}}{{{T_s}}} = \frac{{\frac{\pi }{{32}}\left( {d_1^4 - d_2^4} \right)}}{{\frac{\pi }{{32}}\left( {d_s^4} \right)}} = \frac{{d_1^4 - d_2^4}}{{d_s^4}}= \frac{{(d_1^2 - d_2^2)}{(d_1^2 + d_2^2)}}{{d_s^4}}\)

\(\frac{{{T_h}}}{{{T_s}}} = \frac{{d_1^2 + d_2^2}}{{d_s^2}}\)

दी गई स्थिति के लिए ‘d1’, ‘ds’ से हमेशा अधिक होगा, अतः \(\frac{{{T_h}}}{{{T_s}}} > 1\)
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