Questions in Motion in A Plane

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A body slides down a frictionless track which ends in a circular loop of diameter \[D\], then the minimum height \[h\] of the body in term of \[D\] so that it may just complete the loop, is
A car is moving with speed 30 \[m/\sec \]on a circular path of radius 500 m. Its speed is increasing at the rate of \[2m/{\sec ^2},\] What is the acceleration of the car
The string of pendulum of length \[l\] is displaced through \[{90^o}\] from the vertical and released. Then the minimum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is
A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is revolved in a circular path of radius 2 m in a vertical plane. If \[g = 10m/{s^2}\], then the maximum angular velocity of the stone will be
A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance h below the highest point such thatQuestion Image
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
A weightless thread can bear tension upto 3.7 kg wt. A stone of mass 500 gms is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If \[g = 10\,m{s^{ - 2}}\], then the maximum angular velocity of the stone will be
The maximum velocity at the lowest point, so that the string just slack at the highest point in a vertical circle of radius \[l\]
If the equation for the displacement of a particle moving on a circular path is given by \[(\theta ) = 2{t^3} + 0.5\], where \[\theta \] is in radians and \[t\] in seconds, then the angular velocity of the particle after 2 sec from its start is
A body of mass \[m\] hangs at one end of a string of length l, the other end of which is fixed. It is given a horizontal velocity so that the string would just reach where it makes an angle of \[{60^o}\] with the vertical. The tension in the string at mean position is

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