Describe the relationship between the length and period of a pendulum in the language of direct proportions
1 answer:
The period of the pendulum is directly proportional to the square root of the length of the pendulum
Explanation:
The period of a simple pendulum is given by the equation
where
T is the period
L is the length of the pendulum
g is the acceleration of gravity
From the equation, we see that when the length of the pendulum increases, the period of the pendulum increases as the square root of L, . This means that
The period of the pendulum is directly proportional to the square root of the length of the pendulum
From the equation, we also notice that the period of a pendulum does not depend on its mass.
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The rest energy of a particle is
where
is the rest mass of the particle and c is the speed of light.
The total energy of a relativistic particle is
where v is the speed of the particle.
We want the total energy of the particle to be twice its rest energy, so that
which means:
From which we find the ratio between the speed of the particle v and the speed of light c:
So, the particle should travel at 0.87c in order to have its total energy equal to twice its rest energy.
where
The total energy of a relativistic particle is
where v is the speed of the particle.
We want the total energy of the particle to be twice its rest energy, so that
which means:
From which we find the ratio between the speed of the particle v and the speed of light c:
So, the particle should travel at 0.87c in order to have its total energy equal to twice its rest energy.
Answer:
option (a) 0.61 s
Explanation:
Given;
Time taken by the ball to reach the ground = 0.50 s
Let us first calculate the distance through which the ball falls on the ground
from the Newton's equation of motion, we have
where,
s is the distance
a is the acceleration
t is the time
here it is the case of free fall
thus, a = g = acceleration due to gravity
u = initial speed of the ball = 0
on substituting the values, we get
or
s = 1.225 m
Now,
when the elevator is moving up with speed of 1.0 m/s
the initial speed of the ball = -1.0 m/s (as the elevator is moving in upward direction)
thus , we have
or
or
4.9t^2 - t - 1.225 = 0
or
t = 0.612 s
hence, the correct answer is option (a) 0.61 s
Answer:
ℏ
Given:
Principle quantum number, n = 2
Solution:
To calculate the maximum angular momentum, , we have:
(1)
where,
l = azimuthal quantum number or angular momentum quantum number
Also,
n = 1 + l
2 = 1 + l
l = 1
Now,
Using the value of l = 1 in eqn (1), we get:
ℏ