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If a particle moves in a curved path, it must have a component of acceleration

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Important Questions on Kinematics

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If a point charge q is moving in a circle of radius r with speed v, then time period T of the point charge will be
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A car goes around uniform circular track of radius R at a uniform speed v once in every T seconds. The magnitude of the centripetal acceleration is ac. If the car now goes uniformly around a larger circular track of radius 2R and experiences a centripetal acceleration of magnitude 8ac. Then, its time period is
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Two cars S1 and S2 are moving in coplanar concentric circular tracks in the opposite sense with the periods of revolution 3 min and 24 min, respectively. At the time t=0, the cars are the farthest apart. Then, the two cars will be, 
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Two parallel discs are connected by a rigid rod of length L=0.5 m centrally. Each disc has a slit oppositely placed as shown in the figure. A beam of neutral atoms is incident on one of the discs axially at different velocities v, while the system is rotated at angular speed of, 600 rev s-1, so that atoms only with a specific velocity emerge at the other end. Calculate the two largest speeds (in meter/second) of the atoms that will emerge at the other end.

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A particle at a distance of 1 m from the origin starts moving such that drdθ=r, where r,θ are polar coordinates. Then the angle between resultant velocity and tangential velocity component is:
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A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector a, is correctly shown in which of the following figure ?
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When a ceiling fan is switched off, its angular velocity reduces to 50% while it makes 36 rotations. How many more rotations will it make before coming to rest? (Assume uniform angular retardation)
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A particle has initial velocity 2i^+3j^ and acceleration 0.3i^+0.2j^. The magnitude of velocity after 10 seconds will be