Answer:
proof in explanation
Explanation:
First, we will calculate the number of half-lives:
where,
n = no. of half-lives = ?
t = total time passed = 2100 million years
= half-life = 700 million years
Therefore,
Now, we will calculate the number of uranium nuclei left ():
and the rest of the uranium nuclei will become thorium nuclei ()
dividing both:
<u>Hence, it is proven that after 2100 million years there are seven times more thorium nuclei than uranium nuclei in the rock.</u>
Explanation:
Since, the rod is present in vertical position and the spring is unrestrained.
So, initial potential energy stored in the spring is = 0
And, initial potential gravitational potential energy of the rod is .
It is given that,
mass of the bar = 0.795 kg
g = 9.8
L = length of the rod = 0.2 m
Initial total energy T =
Now, when the rod is in horizontal position then final total energy will be as follows.
T =
where, I = moment of inertia of the rod about the end =
Also,
where, = speed of the tip of the rod
x = spring extension
The initial unstrained length is = 0.1 m
Therefore, final length will be calculated as follows.
x' = m
Then, x =
x = m - 0.1 m
= 0.1236 m
k = 25 N/m
So, according to the law of conservation of energy
Putting the given values into the above formula as follows.
v = 2.079 m/s
Thus, we can conclude that tangential speed with which end A strikes the horizontal surface is 2.079 m/s.
Total resultant velocity=5.11-3.27=1.84m/s