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1.
A bob of mass 
is suspended by a massless string of length 
. The horizontal velocity 
at position 
is just sufficient to make it reach the point 
. The angle 
at which the speed of the bob is half of that at 
, satisfies
is suspended by a massless string of length . The horizontal velocity at position is just sufficient to make it reach the point . The angle at which the speed of the bob is half of that at , satisfies
2.
For a particle in uniform circular motion, thee acceleration 
at a point 
on the circle of radius R is (Here is measured from the x-axis)
at a point on the circle of radius R is (Here is measured from the x-axis)
3.
A man can thrown a stone 100 m away. The maximum height to which he can throw vertically is
4.
Roads are banked on curves so that
5.
A piece of wire is bent in the shape of a parabola 
-axis vertical) with a bead of mass 
on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the 
-axis with a constant acceleration 
. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the 
-axis is
-axis vertical) with a bead of mass on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the -axis with a constant acceleration . The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the -axis is