Mechanics> angular-velocity...

A straight, smooth tunnel is dug through a uniform spherical planet of mass density ? P. The tunnel passes through the center of the planet and is perpendicular to the planet''s axis of rotation, which is fixed in space. The planet rotates with a constant angular speed w so that objects in the tunnel have no apparent weight. Find the required angular speed of the planet ?.

Shuvam Shukla , 12 Years ago

Grade 12

1 Answers

SOURAV MISHRA

when you are in a rotating reference frame then you experience the radially outward centrifugal force.

in this case the centrifugal force balances the gravitational force of attraction.

that is G*(4/3)*πr³Pm/r² = mrw².

here m = mass of the particle, r = distance of the particle from the center of the planet along the tunnel that is the radial distance of the particle.

this gives w = {(4/3)*πGP}^(1/2)

Approved

Last Activity: 12 Years ago

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

Three identical balls are placed on a frictionless horizontal surface touching each other. They stick to each other because of adhesive. Another ball of same radius and mass m is placed over the void created by the three balls. Find the forces applied by the balls kept on the floor to each other if the system remains in equilibrium.

mechanics

1 Answer Available

Last Activity: 5 Months ago

A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.

11
21
31
41

mechanics

1 Answer Available

Last Activity: 5 Months ago

A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mm
at the free end, where a small mass of 2 g is positioned. determine
(i) The velocity of the end when passing through the zero position
(ii) The acceleration at maximum displacement
(iii) The maximum kinetic energy of the mass

mechanics

2 Answers Available

Last Activity: 3 Years ago

An object of mass m = 0.25 kg oscillates in a fluid at the end of a vertical spring of spring
constant kH = 85 N/m, see Fig.1. The effect of the fluid resistance is governed by the
damping constant b = 0.07kg/s.
(i) Find the period of the damped oscillation.
(ii) By what percentage does the amplitude of the oscillation decrease in each cycle?

mechanics

1 Answer Available

Last Activity: 3 Years ago

If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0

mechanics

1 Answer Available

Last Activity: 3 Years ago

View all Questions

Mechanics> angular-velocity...

Shuvam Shukla , 12 Years ago

SOURAV MISHRA

LIVE ONLINE CLASSES

Other Related Questions on mechanics

mechanics

A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.11213141

mechanics

mechanics

mechanics

If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0

mechanics

A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.

11
21
31
41