1. √(gR) 2. √(2gR) 3. √(3gR) 4. √(5gR)

Answer: 4. √(5gR) Key idea: at the top the minimum speed satisfies mg=mv_t²/R , so v_t²=gR . Energy conservation from bottom to top (height 2R ): v²=v_t²+4gR=5gR . Minimum entry speed is √(5gR) .

Topic: Motion in a vertical circle· Work, Energy and Power

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop ?

1. \(\sqrt{gR}\)

2. \(\sqrt{2gR}\)

3. \(\sqrt{3gR}\)

4. \(\sqrt{5gR}\)

Doubtly Asked 30 Oct 2026 NEET UG 2016 Phase 1 Practice test neet Save WhatsApp Report

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Answer: 4. \(\sqrt{5gR}\)

Key idea: at the top the minimum speed satisfies \(mg=\dfrac{mv_t^2}{R}\), so \(v_t^2=gR\).

Energy conservation from bottom to top (height \(2R\)): \(v^2=v_t^2+4gR=5gR\). Minimum entry speed is \(\sqrt{5gR}\).

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop ?

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