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A spotlight S rotates in a horizontal plane with a constant angular velocity of 0.1 rad s-1. The spot of the light, P moves along the wall at a distance 3 m. What is the velocity of the spot P when θ=45°?

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Important Questions on Circular Motion

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A particle A moves along a circle of radius, R=50 cm so that its radius vector r, relative to the point O (figure), rotates with the constant angular velocity, ω=0.40 rad s-1. Then, the modulus of the velocity v of the particle and the modulus of its total acceleration a will be,

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A particle of mass m moves along a circle of radius R with a normal acceleration varying with time as, ar=at2, where a is a constant. Find the time dependence of the power P, developed by all the forces acting on the particle, and the mean value of this power P averaged over a time t after the beginning of the motion.
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A string breaks if its tension exceeds 10 N. A stone of mass 250 g, tied to this string of length 10 cm, is rotated in a horizontal circle. The maximum angular velocity of rotation can be,
MEDIUM
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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,
EASY
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A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to -kr2. The total kinetic energy of the particle is,
MEDIUM
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A stone is projected with speed u and angle of projection is θ. Find the radius of curvature at t=0.
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The velocity and acceleration vectors of a particle undergoing circular motion are v=2i^ m s-1 and a=2i^+4j^ m s-2, respectively, at an instant of time. The radius of the circle is,
HARD
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A particle is projected horizontally from the top of a tower with a velocity v0. If v is its velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to,