जब किसी पिंड का संवेग (momentum) दोगुना कर दिया जाता है, तो उसकी गतिज ऊर्जा ___________
उत्तर और चरणबद्ध हल
स्थिर द्रव्यमान के लिए K=p²/(2m)। संवेग दोगुना करने पर गतिज ऊर्जा 2²=4 गुनी हो जाती है। GPSC की अंतिम उत्तर कुंजी में उत्तर विकल्प C है।
विस्तृत हल (मूल भाषा में)
Concept & Reasoning
Momentum p=mv and kinetic energy K=½mv². Eliminating v gives K=p²/(2m). This square dependence is the quickest way to compare energy after a momentum change without calculating velocity explicitly.
How to Solve It in the Exam
Momentum ×2 → kinetic energy ×4 for same mass.
Important Exam Point
Use final key C; provisional highlighting was revised.
Editorial / Answer-Key Note
The official GPSC final answer key revised the provisional outcome for this question from A to C.
Quick Trick
Momentum ×2 → kinetic energy ×4 for same mass.
Common Mistake
Assuming kinetic energy is directly proportional to momentum.
When the momentum of a body is doubled, its kinetic energy ___________
Answer & step-by-step solution
For constant mass, kinetic energy is K=p²/(2m). Doubling momentum therefore multiplies kinetic energy by 2²=4. The GPSC final key revised the provisional answer to option C.
Concept & Reasoning
Momentum p=mv and kinetic energy K=½mv². Eliminating v gives K=p²/(2m). This square dependence is the quickest way to compare energy after a momentum change without calculating velocity explicitly.
How to Solve It in the Exam
Momentum ×2 → kinetic energy ×4 for same mass.
Important Exam Point
Use final key C; provisional highlighting was revised.
Editorial / Answer-Key Note
The official GPSC final answer key revised the provisional outcome for this question from A to C.
Quick Trick
Momentum ×2 → kinetic energy ×4 for same mass.
Common Mistake
Assuming kinetic energy is directly proportional to momentum.
જ્યારે કોઈ પદાર્થનું વેગમાન (momentum) બમણું કરવામાં આવે, ત્યારે તેની ગતિ ઊર્જા ___________
જવાબ અને પગલાવાર ઉકેલ
અચળ દળ માટે K=p²/(2m). વેગમાન બમણું કરતાં ગતિ ઊર્જા 2²=4 ગણી થાય છે. GPSC ની અંતિમ આન્સર કીમાં જવાબ વિકલ્પ C છે.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Concept & Reasoning
Momentum p=mv and kinetic energy K=½mv². Eliminating v gives K=p²/(2m). This square dependence is the quickest way to compare energy after a momentum change without calculating velocity explicitly.
How to Solve It in the Exam
Momentum ×2 → kinetic energy ×4 for same mass.
Important Exam Point
Use final key C; provisional highlighting was revised.
Editorial / Answer-Key Note
The official GPSC final answer key revised the provisional outcome for this question from A to C.
Quick Trick
Momentum ×2 → kinetic energy ×4 for same mass.
Common Mistake
Assuming kinetic energy is directly proportional to momentum.
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