Via the half-life equation:

Where the time elapse is 11,460 year and the half-life is 5,730 years.

Therefore after 11,460 years the amount of carbon-14 is one fourth (1/4) of the original amount.
To solve the problem it is necessary to use Newton's second law and statistical equilibrium equations.
According to Newton's second law we have to

where,
m= mass
g = gravitational acceleration
For the balance to break, there must be a mass M located at the right end.
We will define the mass m as the mass of the body, located in an equidistant center of the corners equal to 4m.
In this way, applying the static equilibrium equations, we have to sum up torques at point B,

Regarding the forces we have,

Re-arrange to find M,



Therefore the maximum additional mass you could place on the right hand end of the plank and have the plank still be at rest is 16.67Kg
<h2>Acceleration due to gravity in moon is 1.5 m/s²</h2>
Explanation:
We have equation of motion s = ut + 0.5 at²
Here the ball travels 3 m less distance in fifth second compared to third second.
That is
s₃ = s₅ + 3
Now we have
Distance traveled in third second, s₃ = u x 3 - 0.5 x g x 3² - u x 2 - 0.5 x g x 2²
s₃ = u - 2.5 g
Also
Distance traveled in fifth second, s₅ = u x 5 - 0.5 x g x 5² - u x 4 - 0.5 x g x 4²
s₅ = u - 4.5 g
That is
u - 2.5 g = u - 4.5 g + 3
2 g = 3
g = 1.5 m/s²
Acceleration due to gravity in moon = 1.5 m/s²
Answer:
9m^3
Explanation:
Given data
volume v1= 3m^3
volume v2= ???
Temperature T1= 20.0°C.
Temperature T2= 60.0°C.
Applying the relation for temperature and volume
V1/T1= V2/T2
substitute
3/20= V2/60
3*60= V2*20
180= 20*V2
180/20= V2
V2= 9m^3
Hence the final volume is 9m^3