Home
Class 11
PHYSICS
Let omega be the angular velocity of the...

Let `omega` be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth `d` below earth's surface at a pole `(dlt ltR)`. the value of `d` is-

A

`(omega^(2)R^(2))/g`

B

`(omega^(2)R^(2))/(2g)`

C

`(2omega^(2)R^(2))/g`

D

`(sqrt(Rg))/g`

Text Solution

Verified by Experts

The correct Answer is:
a
`g_(eff)` due to rotation =`g_(eff)` due to depth `d`
`g-Romega^(2)=g(1-d/R)impliesRomega^(2)=(gd)/R`
`d=(R^(2)omega^(2))/g`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let omega be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed by a spring balance gives the same reading at the equator as at a height h above the poles (h lt lt R) . The value of h is

Use the assumptions of the previous question. An object weighed by a spring balance at the equator gives the same reading as a reading taken at a depth d below the earths surface at a pole (d gt gt R) . The value of d is

The earth rotates about its own axis, then the value of acceleration due to gravity is

If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity on the earth's surface would

The angular velocity of the earth's rotation about its axis is omega . An object weighed by a spring balance gives the same reading at the equator as at height h above the poles. The value of h will be

The acceleration due to gravity at a height h above the surface of the earth has the same value as that at depth d= ____below the earth surface.

If g is acceleration due to gravity at the surface of the earth, then its value at a depth of 1/4 of the radius of the earth is