Answer :
a) Both spheres have the same speed and both reach at the same time.
b) Both spheres will have the same speed at the bottom of the incline.
a) consider the energy conservation and calculate the speed of each sphere
0 + mgH = 1/2mv² + 1/2 Iw² + mgy
Here,
m is mass
g is gravity
H is height
v is velocity
I is inertia
w is the angular velocity
Now potential energy will be zero at the base of the incline (y=0) and there are initial height H then take position 1 to be the top and position 2 to be the generic location.
mg(H-y) = 1/2(mv² + 2/5mr² v²/r²)
v= √(10/7 g (H-y))
So according to the solution, it is clear that velocity is not depending upon the mass or radius of the sphere. Hence both have the same speed and both reach at the same time.
b) According to the result obtained in part (a), both have the same speed at each point along the incline so both will have the same speed at the bottom of the incline.
According to the conservation of energy total kinetic energy will be bottom of the incline is equal to the potential energy at the incline. There are initial potential energy is proportional to the mass sphere so massive spheres have greater kinetic energy.
Learn more about energy conservation here:
https://brainly.com/question/29220242
#SPJ4