The parallel axis theorem relates icm, the moment of inertia of an object about an axis passing through its center of mass, to ip, the moment of inertia of the same object about a parallel axis passing through point p. the mathematical statement of the theorem is ip=icm+md2, where d is the perpendicular distance from the center of mass to the axis that passes through point p, and m is the mass of the object. part a suppose a uniform slender rod has length l and mass m. the moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by icm=112ml2. find iend, the moment of inertia of the rod with respect to a parallel axis through one end of the rod. express iend in terms of m and l. use fractions rather than decimal numbers in your answer. part b now consider a cube of mass m with edges of length a. the moment of inertia icm of the cube about an axis through its center of mass and perpendicular to one of its faces is given by icm=16ma2. (figure 1) find iedge, the moment of inertia about an axis p through one of the edges of the cube express iedge in terms of m and a. use fractions rather than decimal numbers in your answer.

part a.

part b.

I =

Explanation:

Part a.

For the center of mass the moment of inertia is:

Using the parallel axis theorem, we get:

I =

Additionally,

d = L/2

so:

part b.

For the center of mass the moment of inertia is:

Using the parallel axis theorem, we get:

I =

Adittionally, in this case:

d =

so:

I =

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.