Answer:
The speed of its center of mass =
Explanation:
Consider the potential energy at the level of center of mass of rod below the pivot=0
Mass of uniform rod=M
Length of rod=L
The rotational inertia about the end of a uniform rod=
Kinetic energy at the level of center of mass of rod below the pivot=
Kinetic energy at the level of center of mass of rod above the pivot=0
Potential energy at the level of center of mass of rod above the pivot=mgh
We have to find the center of mass ( in terms of g and L).
According to conservation of law of energy
Initial P.E+Initial K.E=Final P.E+Final K.E
Where
I=Moment of inertia
=Angular velocity
Substitute the values then we get
Now, we know that ,
Substitute the values then we get
Hence, the speed of its center of mass =