Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason RAssertion A: A pendulum clock when taken to Mount Everest becomes fast.Reason R: 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 Both A and R are correct and R is the correct explanation of ABoth A and R are correct but R is not the correct explanation of AA is correct but R is not correctA is not correct but R is correct
Question
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason RAssertion A: A pendulum clock when taken to Mount Everest becomes fast.Reason R: 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 Both A and R are correct and R is the correct explanation of ABoth A and R are correct but R is not the correct explanation of AA is correct but R is not correctA is not correct but R is correct
Solution
Both A and R are correct and R is the correct explanation of A.
Here's why:
A pendulum clock works on the principle of simple harmonic motion. The time period of the pendulum is given by T=2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity.
When the pendulum clock is taken to Mount Everest, the value of g decreases because the acceleration due to gravity is less at higher altitudes.
According to the formula, if g decreases, the time period T should increase. But an increase in time period means the clock slows down. However, the assertion A states that the clock becomes fast, which seems contradictory.
The resolution to this apparent contradiction lies in the construction of the pendulum clock. The clock mechanism is designed to count "ticks" and "tocks" as one second. If the pendulum swings slower (increased time period), the clock mechanism compensates and advances the clock faster.
So, in effect, when taken to a place with lower g (like Mount Everest), a pendulum clock will run faster, which makes the assertion A correct.
And since this is due to the change in g, the reason R is the correct explanation of A.
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