Two stones of masses \(m\) and \(2m\) are whirled in horizontal circles, the heavier one in a radius \(\frac{r}{2}\) and the lighter one in a radius \(r\). The tangential speed of lighter stone is \(n\) times that of the value of heavier stone when they experience the same centripetal forces. The value of \(n\) is:

1. \(3\) 2. \(4\)
3. \(1\) 4. \(2\)
Subtopic:  Uniform Circular Motion |
From NCERT
NEET - 2015
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A car is moving in a circular horizontal track of radius \(10\) m with a constant speed of \(10\) m/s. A bob is suspended from the roof of the car by a light wire of length \(1.0\) m. The angle made by the wire with the vertical is: 
1. \(\pi \over 3 \) 2. \(\pi \over 6\)
3. \(\pi \over 4\) 4. \(0^\circ\)
Subtopic:  Uniform Circular Motion |
 70%
From NCERT
NEET - 2013
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A roller coaster is designed such that riders experience "weightlessness" as they go around the top of a hill whose radius of curvature is \(20\) m. The speed of the car at the top of the hill is between:
1. \(14\) m/s and \(15\) m/s
2. \(15\) m/s and \(16\) m/s
3. \(16\) m/s and \(17\) m/s
4. \(13\) m/s and \(14\) m/s
Subtopic:  Uniform Circular Motion |
 71%
From NCERT
AIPMT - 2008
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A tube of length \(\text L\) is filled completely with an incompressible liquid of mass \(\text M\) and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is:

1. \(ML \omega^2 \over 2\) 2. \(ML^2 \omega \over 2\)
3. \(ML \omega^2 \) 4. \(ML^2 \omega^2 \over 2\)
Subtopic:  Uniform Circular Motion |
 57%
From NCERT
AIPMT - 2006
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