Question
Download Solution PDFपृथ्वीच्या (वस्तुमान M आणि त्रिज्या R) पृष्ठभागावरील गुरुत्वीय त्वरण _________ शी समानुपाती असते.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFयोग्य उत्तर M/R2 आहे.
Key Points
- गुरुत्वाकर्षणामुळे वस्तूवर कार्य करणारे बल f = mg द्वारे दिले जाते.
- जिथे f हे वस्तूवर कार्य करणारे बल आहे, g हे गुरुत्वीय त्वरण आहे आणि m हे वस्तुचे वस्तुमान आहे.
- सार्वत्रिक गुरुत्वाकर्षणाच्या नियमानुसार,
- f = GmM/(r+h)2.
- जिथे,
- f = दोन वस्तूंमधील बल,
- G = सार्वत्रिक गुरुत्व स्थिरांक (6.67×10-11 Nm2/kg2)
- m = वस्तूचे वस्तुमान,
- M = पृथ्वीचे वस्तुमान,
- r = पृथ्वीची त्रिज्या.
- h = पृथ्वीच्या पृष्ठभागापासून वस्तूची उंची.
- पृथ्वीच्या त्रिज्येच्या सापेक्ष उंची (h) नगण्य असल्याने, आपण खालीलप्रमाणे समीकरण पुनरावृत्ती करतो,
- f = GmM/r2
- आता दोन्ही पदावली संतुलित करा,
- mg = GmM/r2
- ⇒ g = GM /r2
- म्हणून, गुरुत्वीय त्वरणाचे सूत्र g = GM/r2 द्वारे दिले जाते
Last updated on Jun 11, 2025
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