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The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by the relation of this type f=cm^xk^y where c is a dimensionless quantity the value of x and y are:-. A . x=1/2 , y=1/2 B. x=-1/2,y=1/2 Please solve this.?
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Solution:
Given, f = cm^xk^y
We need to find the values of x and y.
Let's analyze the given equation.
Let's assume that the mass m and spring constant k have some units.
Let the unit of mass be [M] and the unit of spring constant be [K].
Now, let's write the dimensions of each term in the given equation.
Dimension of f = [T^-1] (as frequency is the reciprocal of time)
Dimension of m^x = [M^x]
Dimension of k^y = [K^y]
Now, equating the dimensions of both sides of the equation, we get:
[T^-1] = [M^x][K^y]
Dimensionally, the left-hand side of the equation has only one term, [T^-1]. Therefore, the right-hand side should also have only one term.
Thus, we can write:
[T^-1] = [M^x][K^y] = [M^0][L^0][T^-1]
where we have used the fact that time has dimension [T].
Now, equating the powers of different dimensions on both sides, we get:
For [M]: x = 0
For [L]: y = 0
For [T]: -1 = -1
Therefore, the values of x and y are:
x = 0 and y = 0
This implies that the given relation is not dimensionally correct.
Hence, there is no valid combination of x and y that satisfies the given equation.
Answer: None of the given options (A and B) is correct.
Given, f = cm^xk^y
We need to find the values of x and y.
Let's analyze the given equation.
Let's assume that the mass m and spring constant k have some units.
Let the unit of mass be [M] and the unit of spring constant be [K].
Now, let's write the dimensions of each term in the given equation.
Dimension of f = [T^-1] (as frequency is the reciprocal of time)
Dimension of m^x = [M^x]
Dimension of k^y = [K^y]
Now, equating the dimensions of both sides of the equation, we get:
[T^-1] = [M^x][K^y]
Dimensionally, the left-hand side of the equation has only one term, [T^-1]. Therefore, the right-hand side should also have only one term.
Thus, we can write:
[T^-1] = [M^x][K^y] = [M^0][L^0][T^-1]
where we have used the fact that time has dimension [T].
Now, equating the powers of different dimensions on both sides, we get:
For [M]: x = 0
For [L]: y = 0
For [T]: -1 = -1
Therefore, the values of x and y are:
x = 0 and y = 0
This implies that the given relation is not dimensionally correct.
Hence, there is no valid combination of x and y that satisfies the given equation.
Answer: None of the given options (A and B) is correct.
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The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by the relation of this type f=cm^xk^y where c is a dimensionless quantity the value of x and y are:-. A . x=1/2 , y=1/2 B. x=-1/2,y=1/2 Please solve this.?
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The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by the relation of this type f=cm^xk^y where c is a dimensionless quantity the value of x and y are:-. A . x=1/2 , y=1/2 B. x=-1/2,y=1/2 Please solve this.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by the relation of this type f=cm^xk^y where c is a dimensionless quantity the value of x and y are:-. A . x=1/2 , y=1/2 B. x=-1/2,y=1/2 Please solve this.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by the relation of this type f=cm^xk^y where c is a dimensionless quantity the value of x and y are:-. A . x=1/2 , y=1/2 B. x=-1/2,y=1/2 Please solve this.?.
The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by the relation of this type f=cm^xk^y where c is a dimensionless quantity the value of x and y are:-. A . x=1/2 , y=1/2 B. x=-1/2,y=1/2 Please solve this.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by the relation of this type f=cm^xk^y where c is a dimensionless quantity the value of x and y are:-. A . x=1/2 , y=1/2 B. x=-1/2,y=1/2 Please solve this.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by the relation of this type f=cm^xk^y where c is a dimensionless quantity the value of x and y are:-. A . x=1/2 , y=1/2 B. x=-1/2,y=1/2 Please solve this.?.
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