Physics And Measurement Question 19
Question: Assertion: The time period of a pendulum is given by the formula, $ T=2\pi \sqrt{g/l} $ . Reason: According to the principle of homogeneity of dimensions, only that formula is correct in which the dimensions of L.H.S. is equal to dimensions of R.H.S.
Options:
A) If both assertion and reason are true and the reason is the correct explanation of the assertion.
B) If both assertion and reason are true but reason is not the correct explanation of the assertion.
C) If assertion is true but reason is false.
D) If the assertion and reason both are false.
E) If assertion is false but reason is true.
Show Answer
Answer:
Correct Answer: E
Solution:
Let us write the dimension of various quantities on two sides of the given relation.
L.H.S. $ =T=[T],
$ R.H.S. $ =2\pi \sqrt{g/l}=\sqrt{\frac{L{{T}^{-2}}}{L}}=[{{T}^{-1}}] $ (
$ \therefore \ 2\pi $ has no dimension).
As dimensions of L.H.S. is not equal to dimension of R.H.S. therefore according to principle of homogeneity the relation $ T=2\pi \sqrt{g/l} $ is not valid.
