Time period of simple pendulum on earth's surface is ' T '. Its time period becomes ' xT ' when taken to a height R (equal to earth's radius) above the earth's surfa

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Time period of simple pendulum on earth's surface is ' T '. Its time period becomes ' xT ' when taken to a height R (equal to earth's radius) above the earth's surface. Then the value of ' x ' will be

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T = 2 π g l ​ ​ At a height 'h' from earth's surface, ∴ ∴ ∴ ∴ ​ xT = 2 π g h ​ l ​ ​ x = g h ​ g ​ ​ … .. ( i ) Now, g h ​ = ( R + h ) 2 GM ​ g h ​ = 4 R 2 GM ​ g h ​ = 4 g ​ From equations (i) and (ii), x = g /4 g ​ ​ = 4 ​ = 2 ​ ∴ From equations (i) and (ii), x = g /4 g ​ ​ = 4 ​ = 2

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