Question

A pendulum clock is taken 1 km inside the earth from mean sea level. Then the pendulum clock
Loses 13.5 sec per day
Gains 13.5 sec per day
Loses 7 sec per day
Gains 7 sec per day​​​​
​Pls provide the answer with appropriate method and along with calculation and also explain step by step ...pls

Answer 1

answer : option (1) 13.5 sec per day

first of all, find acceleration due to gravity.

i.e., g' = g(1 - d/R)

here, d = 1km, R = 6400 km

so, g' = g(1 - 1/6400)

∆g =g - g' = g/6400 = (0.00015625)g

we know time period is inversely proportional to square root of g.

i.e., T ∝ 1/√g

⇒∆T/T = 1/2 ∆g/g

⇒∆T/(24 hrs) = 1/2 × 0.00015625g/g

⇒∆T = 24 × 0.00015625hrs

= 24 × 3600 × 0.00015625 sec

= 13.5 sec

as decreases the acceleration due to gravity, time period increases. and hence clock losses 13.5 sec per day.

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Answer 2

$\huge\bold\purple{Answer:-}$

13.5 sec per day