The radius of the earth is 6400 km and g=10 ms^-2 . In order that a body of 5 kg weights zero

Name: Problem 685, Chapter 6: JEE Physics
Uploaded: 2021-11-13T10:46:25-08:00
Duration: 2 min 16 s
Channel: Narendra Kumar
Description: The radius of the earth is 6400 km and g=10 ms^-2 . In order that a body of 5 kg weights zero at the equator, the angular speed of the earth is =………rad / sec (A) (1 / 80) (B) [1 /(400)] (C) [1 /(800)] (D) [1 /(600)]

step 1 Hello, in the equation it is given that the radius of the earth is 6 -4 -0 kilometer and Z is 10

Question

The radius of the earth is $6400 \mathrm{~km}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2} .$ In order that a body of $5 \mathrm{~kg}$ weights zero at the equator, the angular speed of the earth is $=\ldots \ldots \ldots \mathrm{rad} / \mathrm{sec}$ (A) $(1 / 80)$ (B) $[1 /(400)]$ (C) $[1 /(800)]$ (D) $[1 /(600)]$

   The radius of the earth is $6400 \mathrm{~km}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2} .$ In order that a body of $5 \mathrm{~kg}$ weights zero at the equator, the angular speed of the earth is $=\ldots \ldots \ldots \mathrm{rad} / \mathrm{sec}$
(A) $(1 / 80)$
(B) $[1 /(400)]$
(C) $[1 /(800)]$
(D) $[1 /(600)]$

JEE Physics

StemEZ 1st Edition

Chapter 6, Problem 685

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Solved by Expert Narendra Kumar

11/13/2021

Step 1

We know that the effective acceleration due to gravity is given by $g_{eff} = g - \omega^2 R \cos^2 \lambda$, where $\omega$ is the angular speed of the earth, $R$ is the radius of the earth, and $\lambda$ is the latitude. At the equator, $\lambda = 0$, so $\cos^2 Show more…

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The radius of the earth is $6400 \mathrm{~km}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2} .$ In order that a body of $5 \mathrm{~kg}$ weights zero at the equator, the angular speed of the earth is $=\ldots \ldots \ldots \mathrm{rad} / \mathrm{sec}$ (A) $(1 / 80)$ (B) $[1 /(400)]$ (C) $[1 /(800)]$ (D) $[1 /(600)]$

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Key Concepts

Centrifugal Force

In a rotating reference frame, the centrifugal force is a pseudo-force that appears to act outward from the center of rotation. It becomes significant when analyzing systems where rotation affects the net force experienced by an object, such as determining the effective weight on a rotating body.

Angular Velocity in Rotational Dynamics

Angular velocity is a measure of the rate of rotation expressed in radians per second. It links the rotational motion of an object to the centrifugal force experienced, which increases with the square of the angular speed and with the radius of the circular path.

Gravitational Force

Gravitational force is the attractive force that a massive object, like a planet, exerts on objects near its surface. It provides the acceleration due to gravity that acts downward, and in scenarios involving rotation, it can be counteracted by the centrifugal effect, potentially reducing the effective weight of an object.

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