A simple pendulum has a time period ${T_1}$ when on the earth’s surface and ${T_2}$ when taken to a height $R$ above the earth’s surface, where $R$ is the radius of the earth. The value of ${T_2}/{T_1}$ is
A simple pendulum has a time period ${T_1}$ when on the earth’s surface and ${T_2}$ when taken to a height $R$ above the earth’s surface, where $R$ is the radius of the earth. The value of ${T_2}/{T_1}$ is
$1$
$\sqrt 2 $
$4$
$2$
A simple pendulum has a time period ${T_1}$ when on the earth’s surface and ${T_2}$ when taken to a height $R$ above the earth’s surface, where $R$ is the radius of the earth. The value of ${T_2}/{T_1}$ is
If acceleration due to gravity is $g$ at the surface of earth then at height $R$ it value becomes
$g' = g{\left( {\frac{R}{{R + h}}} \right)^2} = \frac{g}{4}$
${T_1} = 2\pi \sqrt {\frac{l}{g}} {\rm{ and }}\,{T_2} = 2\pi \sqrt {\frac{l}{{g/4}}} $
$\frac{{{T_2}}}{{{T_1}}} = 2$
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