Consider a particle of mass m suspended by a string at the equator. Let R and M denote radius and mass of the earth. If ω is the angular velocity of rotation of the earth about its own axis, then the

Question

Consider a particle of mass m suspended by a string at the equator. Let R and M denote radius and mass of the earth. If ω is the angular velocity of rotation of the earth about its own axis, then the tension on the string will be c o s 0 o = 1

TestHub · Accepted Answer

When a body suspended by the string situated at position $P$ as shown in the figure, where latitude is $λ$ , then body is also rotated with angular frequency $(ω)$ of earth, hence tension on the string is given by

$T = m g - m ω^{2} c o s λ$
$T = m . \frac{G M}{R^{2}} - m ω^{2} c o s λ [∴ g = \frac{G M}{R^{2}}]$
$T = \frac{G M m}{R^{2}} - m r ω^{2} c o s λ$ …. (i)
When body is suspended at equator, then
$λ = 0$ and $r = R$
$∴$ From Eq. (i), we have,
$T = \frac{G M m}{R^{2}} - m R ω^{2} c o s 0^{o}$
$T = \frac{G M m}{R^{2}} - m R ω^{2}$

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