When a wave strikes and object and bounces off . ( example echo)
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The frequency of the nth-harmonic of a string is given by
where n is the number of the harmonic, L is the length of the string, T the tension and
the linear density.
In our problem, since the mass m is tied to the string, the tension is equal to the weight of the object tied:
Substituting into the first formula, we have
In our problem we have n=2 (second harmonic). In the previous equation, the only factor which is not constant between the first and the second part of the problem is m, the mass. So, we can rewrite everything as
where we called
In the first part of the problem, the mass of the object is m and
. So we can write
When the mass is increased with an additional 1.2 kg, the relationship becomes
By writing K in terms of m in the first equation, and subsituting into the second one, we get
and solving this, we find
where n is the number of the harmonic, L is the length of the string, T the tension and
In our problem, since the mass m is tied to the string, the tension is equal to the weight of the object tied:
Substituting into the first formula, we have
In our problem we have n=2 (second harmonic). In the previous equation, the only factor which is not constant between the first and the second part of the problem is m, the mass. So, we can rewrite everything as
where we called
In the first part of the problem, the mass of the object is m and
When the mass is increased with an additional 1.2 kg, the relationship becomes
By writing K in terms of m in the first equation, and subsituting into the second one, we get
and solving this, we find
If Earth’s distance from the sun increased by 4 times then the speed of Earth’s orbit around the sun would decrease by a factor of 2.
Answer: Option 3
<u>Explanation:</u>
From Newton’s second law of motion, it is known that any kind of external force acting on an object will be equal to object’s mass and acceleration exerted on the object. So in this case, the gravitational force between Earth and Sun will be equal to the mass (M) and acceleration exerted on Earth.
It is known that,
Thus, substituting this, we get,
Also, we know,
Then, comparing both the equation, we get the orbital velocity as,
So, here G is gravitational constant, M is the mass of Sun and r is the distance of separation of Earth from Sun.
If the distance of Earth from Sun increases by 4 times so r’ will be 4r. Thus the new orbital velocity v’ will be
So,
Thus, the orbital speed will be decreased by a factor of 2 when the distance of Earth from the Sun increased by 4 times.