Questions in Motion in A Plane

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A particle of mass \[m\] is executing uniform circular motion on a path of radius \[r\]. If \[p\] is the magnitude of its linear momentum. The radial force acting on the particle is
A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance \['r'\]. The speed of the particle is
Two masses \[M\] and \[m\] are attached to a vertical axis by weightless threads of combined length \[l\]. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity \[\omega \]. If the tensions in the threads are the same during motion, the distance of \[M\] from the axis is
A boy on a cycle pedals around a circle of 20 metres radius at a speed of \[20\,metres/\sec .\] The combined mass of the boy and the cycle is 90 kg. The angle that the cycle makes with the vertical so that it may not fall is \[(g = 9.8\,m/{\sec ^2})\]
The average acceleration vector for a particle having a uniform circular motion is
Radius of the curved road on national highway is \[R\]. Width of the road is \[b\]. The outer edge of the road is raised by \[h\] with respect to inner edge so that a car with velocity \[v\] can pass safe over it. The value of \[h\] is
When a particle moves in a uniform circular motion. It has
A motorcycle is going on an overbridge of radius $R$ The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it
A mass of 2 kg is whirled in a horizontal circle by means of a string at an initial speed of 5 revolutions per minute. Keeping the radius constant the tension in the string is doubled. The new speed is nearly
The magnitude of the centripetal force acting on a body of mass \[m\] executing uniform motion in a circle of radius \[r\] with speed \[v\] is

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