A particle of mass m moves in a vertical circle of radius R on the inside of a smooth circular track — JEE Physics
A particle of mass $m$ moves in a vertical circle of radius $R$ on the inside of a smooth circular track. Find the minimum speed at the top of the circle so the particle maintains contact with the track.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
▲ 26
At the top, normal force $N \geq 0$. Applying Newton's second law toward the center:
$$mg + N = \frac{mv^2}{R}$$
For minimum speed, $N = 0$:
$$mg = \frac{mv_{min}^2}{R} \Rightarrow v_{min} = \sqrt{gR}$$
$$v_{min} = \sqrt{gR}$$
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Discussion (4)
A
Tip for others: you can verify the answer quickly by checking the units.
SG
Brilliant explanation, the substitution step is what I kept missing.
M
Is there a faster shortcut for this in the actual exam? Time is tight.
VA
Great discussion here. If you want more practice on this concept, check the related questions in this category.