Is it a Projectile?
A smooth cylindrical log of wood of radius R meter is fixed on a horizontal surface. The minimum speed with which a particle should be projected to reach other side is where g is acceleration due to gravity. Find x.
Try more from my set Classical Mechanics Problems .
The answer is 4.
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For the particle to reach the other side it should cross the top of the log with minimum possible speed.
Now just think reversely. What will happen if someone at the top of log gently disturb a particle?
At some point on the log, the particle will leave and start doing projectile motion and it hits the ground at some point with speed 4 g R and at some angle with horizontal.
Now if we throw a particle with same speed, at same angle from horizontal and from the same point on the ground, it will retraces its previous path and reach the top of the log.
And if the speed is just greater than 4 g R , the particle will go to the top of the log with some velocity and finally reach the other end.