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JEE Main 202324 JanuaryEvening Shift
Exam
JEE Main
Year
2023
Date
24 January
Shift
Evening Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2023 · 24 January · Evening Shift · Physics · Gravitation

Given below are two statements: one is labelled as Assertion A and...

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion AA: A pendulum clock when taken to Mount Everest becomes fast.

Reason RR: The value of g (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth.

In the light of the above statements, choose the most appropriate answer from the options given below

Options

  1. ABoth AA and RR are correct and RR is the correct explanation of AA
  2. BBoth AA and RR are correct but RR is not the correct explanation of AA
  3. CAA is correct but RR is not correct
  4. DAA is not correct but RR is correct

Correct answer

D. AA is not correct but RR is correct

Step-by-step solution

Time period of a pendulum is given by T=2πLgT = 2\pi\sqrt{\dfrac{L}{g}}, where LL is the length of the pendulum and gg is the acceleration due to gravity.

As, T∝1gT ∝ \dfrac{1}{\sqrt{g}}, so the time period of vibration of the pendulum clock increases i.e. it starts taking more time to complete each vibration. Therefore, the pendulum clock becomes slow.

The acceleration due to gravity decreases with height h(h≪R)abovethesurfaceas:</p><p>h \left(h ≪ R\right) above the surface as:</p><p>{g}^{'} = g\left(1 - \dfrac{h}{R}\right)</p><p>Thus,valueof</p><p>Thus, value ofg is less at Mount Everest than its value on the surface of earth.

Hence, assertion is wrong, but reason is correct.

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