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In a conical  pendulum, the centripetal force $$\left[ \dfrac { { mv }^{ 2 } }{ r }  \right] $$ acting on the bob is given by

Figure shows (x, t), (y, t) diagram of a particle in two-dimensions.If the particle has a mass of 500 g, find the force (direction and magnitude) acting on the particle.

A rubber ball is bounced on the floor of a room which has its ceiling at a height of  $$3.2{ m }$$  from the floor. The ball hits the floor with a speed of  $$10 m / { s },$$  and rebounds vertically up. If all collisions simply reverse the velocity of the ball, without changing its speed, then how long does it take the ball for a round trip, from the moment it bounces from the floor to the moment it returns back to it ? Acceleration due to gravity is  $$10 m / s ^ { 2 }.$$

A particle of mass $$m$$, initially at rest is acted upon by a variable force f varying with time t. It begins to move with a velocity u after the force stops acting.)(curve is semi circle )

The maximum and minimum tensions in a string of length 0.1 m with a stone 5 g tied to it and whirled in a vertical circle are in the ratio 13 : 1. The velocity of the body at highest point is 

The potential energy of a particle of mass 1 kg free to move along the x-axis is given by U($$x$$) =($$\frac{x^2}{2}$$-$$x$$) joule. If the total mechanical energy of the particle is 2J, then find the maximum speed of the particle. (Assuming only conservative force acts on the particle)

A body at rest can have

A particle originally at rest at the hoghest point of a smooth vertical circle is slightly displaced. it will leave the circle at a vertical distance h below the highest point, such that h is equal to

The graph below show the force acting on a particle moves along the positive $$x-$$axis from the origin to $$x=x_1$$. The force if parallel to the $$x-$$axis and is conservative. The maximum magnitude $$F_1$$ has the same values for all graphs. Rank the solutions according to the change in the potential energy associated with the force. least (or most negative) to greatest (or most positive)  

A stone of mass $$0.3$$ kg attached to a $$1.5$$m long string is whirled around in a horizontal circle at a speed of $$6$$ m/s. The tension in the string is?