Answer :
The acceleration of center of mass of spherical shell = 2.94 [tex]m/s^{2}[/tex]
What is center of mass ?
A position established in relation to an object or set of objects is the center of mass. It is the average location of all the pieces of the system, weighted according to their masses.
According the given information
Two forces act along the line of motion. Gravity down the slope,
m g sin([tex]\alpha[/tex]), and friction up the slope, F. They provide the linear acceleration and F also provides the torque about the Center of mass. This gives the equations of motion:
m a = m g sin([tex]\alpha[/tex]) - F
I dV/dt = F R
A spherical shell of mass m has moment of inertia I = 2/3 m R^2. Furthermore a pure rolling relates dV/dt and a through a = R dV/dt. So the two equations become
m a = m g sin([tex]\alpha[/tex]) - F
2/3 m a = F
These we solve for a and F:
Substituting F from the second equation gives
m a = m g sin([tex]\alpha[/tex]) - 2/3 m a
a = 3/5 g sin([tex]\alpha[/tex])
a = 3/5 × 9.80m/s^2 sin(30.0) = 2.94 [tex]m/s^{2}[/tex]
The acceleration of center of mass of spherical shell = 2.94 [tex]m/s^{2}[/tex]
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