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इकाई त्रिज्या के अर्द्धगोलाकार आकृति वाले एक समान घनत्व के पदार्थ से बनाए गए ठोस S पर विचार करें:

S = {(x, y, z) | x2 + y2 + z2 ≤ 1 z ≥ 0}.

निम्नलिखित में से कौन-सा कथन सत्य है?

This question was previously asked in
CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  1. S का संहति केंद्र मूल बिंदु पर है
  2. x-अक्ष S के लिए मुख्य अक्ष है
  3. S का जड़त्व आघूर्ण टेंसर एक विकर्णीय आव्यूह नहीं है
  4. z-अक्ष S के लिए मुख्य अक्ष है

Answer (Detailed Solution Below)

Option 4 : z-अक्ष S के लिए मुख्य अक्ष है
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Detailed Solution

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S के लिए z-अक्ष एक मुख्य अक्ष है।

विकल्प (4) सही है।

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Q1.इकाई त्रिज्या के अर्द्धगोलाकार आकृति वाले एक समान घनत्व के पदार्थ से बनाए गए ठोस S पर विचार करें: S = {(x, y, z) | x2 + y2 + z2 ≤ 1  z ≥ 0}. निम्न में से कौन-सा वक्तव्य सत्य है?

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