If the earth is treated as a sphere of radius R and mass M, its angular momentum about the axis of its rotation with period T, is

Question

If the earth is treated as a sphere of radius R and mass M, its angular momentum about the axis of its rotation with period T, is (A) (MR2 T/2π) (B) (4π MR2 /5T) (C) (π MR3 /T) (D) (2π MR2 /T)

Tardigrade Admin · Accepted Answer

The moment of inertia I of a solid sphere about the axis of rotation through the centre is I = (2/5) MR2 ∴ Angular momentum L = Iω = (2/5)MR2×(2π/T) = (4π MR2/5T) where T = time period of rotation.

Q. If the earth is treated as a sphere of radius $R$ and mass $M$ , its angular momentum about the axis of its rotation with period $T$ , is

$\frac{M R ^{2} T}{2 π}$

$\frac{4 π M R ^{2}}{5 T}$

$\frac{π M R ^{3}}{T}$

$\frac{2 π M R ^{2}}{T}$

The moment of inertia $I$ of a solid sphere about the axis of rotation through the centre is
$I = \frac{2}{5} M R^{2}$
$∴$ Angular momentum $L = I ω$
$= \frac{2}{5} M R^{2} \times \frac{2 π}{T}$
$= \frac{4 π M R ^{2}}{5 T}$
where $T =$ time period of rotation.

Q. If the earth is treated as a sphere of radius R and mass M, its angular momentum about the axis of its rotation with period T, is

2πMR2T​

5T4πMR2​

TπMR3​

T2πMR2​