SATHEE: Physics And Measurement Question 66

Physics And Measurement Question 66

Question: The frequency of vibration $f$ of a mass $m$ suspended from a spring of spring constant $K$ is given by a relation of this type $f = C m^{x} K^{y}$ ; where $C$ is a dimensionless quantity. The value of $x$ and $y$ are

[CBSE PMT 1990]

Options:

A) $x = \frac{1}{2}, y = \frac{1}{2}$

B) $x = - \frac{1}{2}, y = - \frac{1}{2}$

C) $x = \frac{1}{2}, y = - \frac{1}{2}$

D) $x = - \frac{1}{2}, y = \frac{1}{2}$

Show Answer

Answer:

Correct Answer: D

Solution:

By putting the dimensions of each quantity both the sides we get $[T^{- 1}] = {[M]}^{x} {[M T^{- 2}]}^{y}$
Now comparing the dimensions of quantities in both sides we get $x + y = 0 and 2 y = 1$

$∴$ $x = - \frac{1}{2}, y = \frac{1}{2}$

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Physics And Measurement Question 66

Question: The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type f=CmxKy ; where C is a dimensionless quantity. The value of x and y are

Options:

Answer:

Solution:

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Question: The frequency of vibration $f$ of a mass $m$ suspended from a spring of spring constant $K$ is given by a relation of this type $f = C m^{x} K^{y}$ ; where $C$ is a dimensionless quantity. The value of $x$ and $y$ are