Amass of 5kg starts from rest and pulls down vertically on a string wound around a disk-shaped, massive pulley. the mass of the disk is 5kg and its radius is 2 m. what is the linear speed, in m/s, after the mass drops by 0.3 m?

a. 0.5
b. 1.5
c. 2
d. 3
e.5

c. V = 2 m/s

Explanation:

Using the conservation of energy:

so:

Mgh =

where M is the mass, g the gravity, h the altitude, I the moment of inertia of the pulley, W the angular velocity of the pulley and V the velocity of the mass.

Also we know that:

V = WR

Where R is the radius of the disk, so:

W = V/R

Also, the moment of inertia of the disk is equal to:

I =

I =

I = 10 kg*m^2

so, we can write the initial equation as:

Mgh =

Replacing the data:

(5kg)(9.8)(0.3m) =

solving for V:

(5kg)(9.8)(0.3m) =

V = 2 m/s

a and b sometimes have a positive value

i don't understand. explain it clearly