Hey JayDilla, I get 1/3. Here's how:
Kinetic energy due to linear motion is:

where

giving

The rotational part requires the moment of inertia of a solid cylinder

Then the rotational kinetic energy is

Adding the two types of energy and factoring out common terms gives

Here the "1" in the parenthesis is due to linear motion and the "1/2" is due to the rotational part. Since this gives a total of 3/2 altogether, and the rotational part is due to a third of this (1/2), I say it's 1/3.
The answer is true: the pressure of a gas will decrease as temperature decreases in a rigid container.
This is one of the central gas laws called the Gay-Lussac law that states for a given gas at a constant volume, the pressure of the gas is directly proportional to its temperature. We also know that as temperature reduces, so too does molecular interaction. Increased temperature results in increased pressure, and decreased temperature therefore results in decreased pressure.
Answer: MR²
is the the moment of inertia of a hoop of radius R and mass M with respect to an axis perpendicular to the hoop and passing through its center
Explanation:
Since in the hoop , all mass elements are situated at the same distance from the centre , the following expression for the moment of inertia can be written as follows.
I = ∫ r² dm
= R²∫ dm
MR²
where M is total mass and R is radius of the hoop .
Here we can use momentum conservation as in this type of collision there is no external force on it

now here we can say




now here we can say


now by coefficient of restitution
for elastic collision we know that e = 1


now by solving the two equation


also we know that

so final speed of the nail is 6.875 m/s