Answer:
Part a)

Part b)

Explanation:
As the uniform sphere is rolling down the inclined plane then the net force on the sphere is given as

also we have torque equation on it

for pure rolling


now we have

now we have


now given that

so we have



Part b)
If the inclined plane is frictionless then the acceleration is given as



If the objects comprise a gas, then the first object contains more
thermal energy (heat) than the second object.
If the objects are solid, then you can't draw any conclusion unless
both objects have the same total mass. If that's the case, then the
first object must be moving faster than the second one.
Answer:
Isotopes can both be the same element but have a different number of electrons
Explanation: not sure if more was supposed to be there, but i tried
The average radius(r) of each grain is r = 50 nanometers
= 50*10^-6 meters
Since it is spherical, so
Volume=(4/3)*pi*r^3
V= (4/3)*pi*(50*10^-6)^3
V=5.23599*10^-13 m^3
We are given the Density(ρ) =2600kg/m^3
We know that:
Density(p) = mass(m)/volume(V)
m = ρV
So the mass of a single grain is:
m = 5.23599*10^-13 * 2600 = 1.361357*10^-9 kg
The surface area of a grain is:
a = 4*pi*r^2
a = 4*pi*(50*10^-6)^2
a = 3.14*10^-8 m^2
Since we know the surface area and mass of a grain, the
conversion factor is:
1.361357*10^-9 kg / 3.14*10^-8 m^2
Find the Surface area of the cube:
cube = 6a^2
cube = 6*1.1^2 = 7.26m^2
multiply this by the converions ratio to get:
total mass of sand grains = (7.26 m^2 * 1.361357*10^-9 kg)
/ (3.14*10^-8 m^2)
total mass of sand grains = 0.3148 kg = 314.80 g
Using current technology, useful parallax measurements can only be found for stars up to about 340 light years (100 parsecs) away.