In the following four periods
$(i)$ Time of revolution of a satellite just above the earth’s surface $({T_{st}})$
$(ii)$ Period of oscillation of mass inside the tunnel bored along the diameter of the earth $({T_{ma}})$
$(iii)$ Period of simple pendulum having a length equal to the earth’s radius in a uniform field of $9.8 \;N/kg \;({T_{sp}})$
$(iv)$ Period of an infinite length simple pendulum in the earth’s real gravitational field $({T_{is}})$
In the following four periods
$(i)$ Time of revolution of a satellite just above the earth’s surface $({T_{st}})$
$(ii)$ Period of oscillation of mass inside the tunnel bored along the diameter of the earth $({T_{ma}})$
$(iii)$ Period of simple pendulum having a length equal to the earth’s radius in a uniform field of $9.8 \;N/kg \;({T_{sp}})$
$(iv)$ Period of an infinite length simple pendulum in the earth’s real gravitational field $({T_{is}})$
${T_{st}} > {T_{ma}}$
${T_{ma}} > {T_{st}}$
${T_{sp}} < {T_{is}}$
${T_{st}} = {T_{ma}} = {T_{sp}} = {T_{is}}$
In the following four periods
$(i)$ Time of revolution of a satellite just above the earth’s surface $({T_{st}})$
$(ii)$ Period of oscillation of mass inside the tunnel bored along the diameter of the earth $({T_{ma}})$
$(iii)$ Period of simple pendulum having a length equal to the earth’s radius in a uniform field of $9.8 \;N/kg \;({T_{sp}})$
$(iv)$ Period of an infinite length simple pendulum in the earth’s real gravitational field $({T_{is}})$
$(i)$ ${T_{st}} = 2\pi \sqrt {\frac{{{{(R + h)}^3}}}{{GM}}} = 2\pi \sqrt {\frac{R}{g}} $ [As $h < < R$ and $GM=gR^2$]
$(ii)$ ${T_{ma}} = 2\pi \sqrt {\frac{R}{g}} $
$(iii)$ ${T_{sp}} = 2\pi \sqrt {\frac{1}{{g\left( {\frac{1}{l} + \frac{1}{R}} \right)}}} = 2\pi \sqrt {\frac{R}{{2g}}} $ [As $l = R]$
$(iv)$ ${T_{is}} = 2\pi \sqrt {\frac{R}{g}} $ $[As\,\,l = \infty ]$
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