Question

Assertion :The frequency of a seconds pendulum in an elevator moving up with an
acceleration half the acceleration due to gravity is $0.612s^{-1}$
Reason :The frequency of a seconds pendulum does not depend upon acceleration due to gravity.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
• C. Assertion is correct but Reason is incorrect.
• D. Both Assertion and Reason are incorrect.

Answer 1

The correct option is C Assertion is correct but Reason is incorrect.

Here it is given that, $a=g/2$

$g_{eff}=g+g/2=3g/2$

$f_{eff}=\frac{1}{2\pi }\sqrt{\frac{g_{eff}}{l}}=\frac{1}{2\pi }\sqrt{\frac{3g}{2R}}$
$=\sqrt{\frac{3}{2}}\times \frac{1}{2}se{c}^{-1}$
$=0.612se{c}^{-1}$
Frequency is dependent on the acceleration due to gravity as $f$ is directly proportional to $\sqrt{g}$