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A particle \((1),\) dropped from rest from the topmost point \((A)\) of a vertical circle, reaches the bottom \((B)\) in the same time as when a second particle \((2)\) moving with constant speed moves along the circumference from \(A\) to \(B.\) The ratio of the accelerations of the particles \((a_1/a_2)\) equals:
                            

 
1. \(1\) 2. \(\dfrac{2}{\pi} \)
3. \(\dfrac{4}{\pi^2} \) 4. \(\sqrt{\dfrac{2}{\pi}} \)

Subtopic:  Circular Motion |
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Match the shapes of the paths in Column I with the possible accelerations mentioned under Column II.
Column I Column II
\(\mathrm{(A)}\) Straight line \(\mathrm{(I)}\) \(\vec a=\text{constant}\)
\(\mathrm{(B)}\) Circle \(\mathrm{(II)}\) \(a_t~\text{(tangential)}=0\\ a_c~\text{(centripetal)}\neq0\)
\(\mathrm{(C)}\) Parabola \(\mathrm{(III)}\) \(a_t~\text{(tangential)}\neq0\\ a_c~\text{(centripetal)}=0\)
\(\mathrm{(D)}\) Ellipse \(\mathrm{(IV)}\) \(a_t~\text{(tangential)}\neq0\\ a_c~\text{(centripetal)}\neq0\)
 
1. \(\mathrm{A\text-I,III;B\text-II,IV;C\text-I,II,IV;D\text-II,IV}\)
2. \(\mathrm{A\text-I;B\text-II,IV;C\text-I,IV;D\text-I,IV}\)
3. \(\mathrm{A\text-II,IV;B\text-I,III;C\text-II,IV;D\text-III,IV}\)
4. \(\mathrm{A\text-I;B\text-II,III;C\text-II;D\text-IV}\)
Subtopic:  Circular Motion |
From NCERT

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Two particles \(A,B\) move along the periphery of a circle of radius \(R,\) with the same uniform speed \(u.\) Particle \(A\) follows \(B,\) a quarter of the circumference behind it. The acceleration of \(A\) relative to \(B\) is:
1. zero 2. \(\dfrac{2u^2}{R}\)
3. \(\dfrac{u^2}{\sqrt2R}\) 4. \(\dfrac{\sqrt2u^2}{R}\)
Subtopic:  Circular Motion |
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A tangential force, constant in magnitude, acts on a particle moving in a circular path. This kind of force is:
1. conservative
2. non-conservative
3. neither conservative nor non-conservative
4. either conservative or non-conservative depending on whether the force is acting forward or backward
Subtopic:  Circular Motion |
From NCERT

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Two particles \(A\) and \(B\) start moving uniformly along the periphery of a circle, \(A\) making \(2\) revolutions/min and \(B\) making \(3\) revolutions/min. \(A\) and \(B\) start from the same point, moving in opposite directions. After what minimum time will they meet at their starting point? 
1. \(1\) min 
2. \(6\) min
3. \(0.5\) min 
4. \(\dfrac {1}{6}\) min
Subtopic:  Circular Motion |
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A particle is released from the top of a smooth hemisphere of radius \(R,\) and it slides down along its surface. After it slides down a height \(\frac R5,\) its acceleration will be \(a,\) where: 
   
1. \(a<\dfrac{2 g}{5}\)
2. \(\dfrac{2 g}{5}< a< \dfrac{3 g}{5}\)
3. \(\dfrac {3g} {5} <a<g\)
4. \(a = g \)
Subtopic:  Circular Motion |
From NCERT

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