After three half-lives have elapsed, the amount of an 8.0 g sample of a radionuclide that remains undecayed is 1.0 g.
<h3>What is Half-Life?</h3>
Half-Life refers to the time it takes for half the amount of a substance to disappear or change.
The nucleus of the atoms of radioactive elements disintegrate to half their starting amounts after every Half-Life.
After three half-lives one-eight of the original atoms remain.
Therefore, after three half-lives have elapsed, the amount of an 8.0 g sample of a radionuclide that remains undecayed is 1.0 g.
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D. There is a known constant concentration of C14 in Nature. As we consume living things to survive our bodies (made of carbon) stop replenishing our body's carbon (we stop eating) and start to decay. Since we know the 1/2 life of C14 and the ratio of C14 to normal C12 we can determine fairly accurately how long ago a thing stopped consuming carbon (e.g. when it died)
Answer:
Explanation:
Given
Mass of alice 
Mass of bob 
Mass of beam 
Suppose fulcrum is at distance of d from bob thus From diagram
Equating torque i.e. torque of Bob,Alice and beam must cancel out each other to be balanced




Answer:
See the answers below
Explanation:
To solve this problem we must use the following equation of kinematics.

where:
Vf = final velocity [m/s]
Vo = initial velocity [m/s]
a = acceleration [m/s²]
t = time [s]
<u>First case</u>
Vf = 6 [m/s]
Vo = 2 [m/s]
t = 2 [s]
![6=2+a*2\\4=2*a\\a=2[m/s^{2} ]](https://tex.z-dn.net/?f=6%3D2%2Ba%2A2%5C%5C4%3D2%2Aa%5C%5Ca%3D2%5Bm%2Fs%5E%7B2%7D%20%5D)
<u>Second case</u>
Vf = 25 [m/s]
Vo = 5 [m/s]
a = 2 [m/s²]
![25=5+2*t\\t = 10 [s]](https://tex.z-dn.net/?f=25%3D5%2B2%2At%5C%5Ct%20%3D%2010%20%5Bs%5D)
<u>Third case</u>
Vo =4 [m/s]
a = 10 [m/s²]
t = 2 [s]
![v_{f}=4+10*2\\v_{f}=24 [m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3D4%2B10%2A2%5C%5Cv_%7Bf%7D%3D24%20%5Bm%2Fs%5D)
<u>Fourth Case</u>
Vf = final velocity [m/s]
Vo = initial velocity [m/s]
a = acceleration [m/s²]
t = time [s]
![v_{f}=5+8*10\\v_{f}=85 [m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3D5%2B8%2A10%5C%5Cv_%7Bf%7D%3D85%20%5Bm%2Fs%5D)
<u>Fifth case</u>
Vf = final velocity [m/s]
Vo = initial velocity [m/s]
a = acceleration [m/s²]
t = time [s]

The total moment of inertia about an axis is :
for a ring of mass m and radius straight r attached to a thin rod.
<h3>
Determine the Total moment of Inertia about an axis </h3>
<u>Given data:</u>
mass of ring --> m
radius of ring --> r
mass of rod --> M
Length of rod ---> L ( 2 * radius )
Total Moment of Inertia about an axis = Irod + Iring
where : Irod = moment of inertia of rod, Iring = moment of inertia of ring
Irod = ML² / 3
Iring = 2mr² / 5
moment of inertia around an axis by Iring = I
where ; I = 2mr² / 5 + ML² according to parallel axis theorem
Hence the Total moment of Inertia about an axis is :
Itotal = 2mr²/5 + ML² + ML² / 3
= 
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