if earth is treated as a uniform solid sphere of radius r and mass m. its angular momentum about the axis of rotation with period t is

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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

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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

5T 4πMR 2 ​

B

5T 2πMR 2 ​

C

T MR 2 T ​

D

T πMR 3 ​ Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is A)

Angular momentum = Iω=

5 2 ​ MR 2 . T 2π ​ = 5T 4πMR 2 ​

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

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

Byju's Answer Standard XII Physics Rotational Inertia If the earth ... Question

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

A M R 2 T 2 π B 4 π M R 2 5 T C π M R 3 T T D 2 π M R 2 T Open in App Solution

The correct option is B

4 π M R 2 5 T

The moment of inertia

I

of a solid sphere about the axis of rotation through the centre is

I = 2 5 M R 2 ∴ Angular momentum, L = I ω = 2 5 M R 2 × 2 π T = 4 π M R 2 5 T

where T = Time period of rotation.

Hence, the correct answer is option (b).

Rotational Inertia

Standard XII Physics

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SIMILAR QUESTIONS

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:

Q. The value of angular momentum of the earth rotating about its own axis is : (Mass of the earth=

5.978 × 10 24 k g

and Radius of earth=

6.378 × 10 6 m )

Q. The angular momentum of a hollow sphere of radius R about an axis, passing through its centre of mass perpendicular to the plane and rotating with an angular velocity

ω will be:

Q. A uniform sphere of mass

m , radius r

and momentum of inertia

I

about its centre moves along the x-axis as shown in figure. Its centre of mass moves with velocity

= v 0

, and it rotates about its centre of mass with angular velocity

= ω 0 . Let → L = ( I ω 0 + m v 0 r ) ( − k )

. The angular momentum of the body about the origin

O is

Q. If the angular momentum of a particle of mass

m

is rotating along a circular path of radius

r

with uniform speed. Its angular momentum about the axis of rotation is

L

, the centripetal force acting on the particle is :

View More

स्रोत : byjus.com

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

The moment of inertia I of a solid sphere about the axis of rotation through the centre is I=(2)/(5)MR^(2) therefore Angular momentum L=Iomega=(2)/(5)MR^(2)xx(2pi)/(T) =(4piMR^(2))/(5T) where T=time period of rotation.

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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

Updated On: 27-06-2022

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Text Solution Open Answer in App A M R 2 T 2π MR2T2π B 4πM R 2 5T 4πMR25T C πM R 2 T πMR2T D 2πM R 2 T 2πMR2T Answer

The correct Answer is B

Solution

The moment of inertia I of a solid sphere about the axis of rotation through the centre is

I= 2 5 M R 2 I=25MR2 ∴ ∴ Angular momentum L=Iω= 2 5 M R 2 × 2π T L=Iω=25MR2×2πT = 4πM R 2 5T =4πMR25T

where T=time period of rotation.

Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Transcript

hello everyone we can be treated as a sphere of radius R and mass M Momentum about this and this is the formula of angular momentum is in the form of a sphere so is 25

Omega is angle cover so when we calculate the value of this point that option is the right answer

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