This is referred to as a "physical pendulum" problem. The equation you need, to relate the period P to the geometry, can be found at
http://hyperphysics.phy-astr.gsu.edu/HBASE/pendp.html
In this case, it becomes
P = 2 pi sqrt[I/(M g R)]
where I is the moment of inertia for oscillating about the nail.
Use the parallel axis therorm to derive the relation
I = 2 MR^2
M cancels out and you are left with
P = 2 pi sqrt(2R/g)
From P you can calculate R.
Use conservation of energy to get the maximum oscillation speed, going through the equilibrium position.
You will need to equate the potential energy rise at maximum swing angle to the kinetic energy (1/2) I w^2 at the equilibrium position.
(c) At the equilibrium position, the acceleration of a particle is centripetal. Use the maximum velocity to compoute it.
(d) At the extreme position, acceleration is tangential. Maximum angular acceleration equals w times maximum angular velocity
This is a rather long problem and I will leave you go through the computational steps and verfy my logic.
A closed circular wire hung on a nail in awall undergoes small oscillations 2 degree & the time period 2sec.Find (a) the radius of the circular wire (b)the speed of the particle farthest away from the point of suspension as it goes through the mean position (c) the acceleration of this particle as it goes through the mean positon &(d)acceleration of this particle when it is at the exterme position.Take g = pi^2m/sec^2
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