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Upto what height above the ground should a pendulum be taken so that its time period doubled?
Asked by brijk456 | 16 Aug, 2019, 11:18: AM
answered-by-expert Expert Answer
Time priod begin mathsize 12px style T space proportional to space fraction numerator 1 over denominator square root of g end fraction end style
if period is doubled means g will be reduced to (1/4)g  .
 
from the definition of acceleration due to gravity,  we have at a height h above earth surface, 
 
g' = GM/(R+h)2 ................(1)
 
where g' is acceleration due to gravity at height h above the earth surface, G is universal gravitation constant,
M is mass of earth and R is radius of earth.
 
Since we want at height h, acceleration due to gravity is (1/4)th of that at earth surface, then we have
 
GM/(R+h)2 = (1/4) GM/R2   .............................. (2)
 
from eqn.(2),  (R+h) = 2R    or   h = R
 
Hence if we take the pendulam to a height h equals radius of earth,
then we have time period of pendulam is double of that of on earth's surface
 
Answered by Thiyagarajan K | 16 Aug, 2019, 12:33: PM

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