time saver pack 3-better late than never
Hi folks!
Big gap between pack two and three, but its here enjoy:
---------> On any given incline when an object of any mass just starts sliding 
where
is the inclination of the plane from the ground and
is the frictional coefficient.
---------> The bob of a pendulum of effective length l is displaced by an angle
and released.
The speed at the mean position will be 
and maximum height attained on the other side will be 
----------> A plank of mass M and length L, is floating on water, a man of mass m walks from one edge to another of the plank at constant speed.
Resulting displacement of the plank from its position = 
-----------> A uniform rod leans between a wall and the ground.
1 is the frictional coefficient between the rod and the wall,
2 between the rod and the ground. Then smallest angle it can make with the ground without slipping is = 
------------> A bullet of mass m and speed v, strikes a mass M hanging from a point as a pendulum to displace it by an angle 
then the following is the condition for the phenomenon 
-------------> A block slides on the outside of a smooth fixed sphere of radius R. The initial position of the block is at a height of 2R from the ground. Then the block will lose contact with the sphere when its vertical displacement = 
-------------->For any vehicle to move without slipping on a track with frictional coefficient
and any inclination when its velocity is v
please note that here r is the radius of the circular plane of motion of the car that is parallel to the ground.
Comments and rates are invited
For any errors in this article, please nudge me,
with nastiness
Mr. Nasty
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