A particle moves with the speed $v$ in a circular orbit of radius $r$ around a planet. The particle is now moved to another circular orbit of radius $2r$. The new orbital speed is :

A planet has double the mass of earth and half its radius. What is the gravitational field strength on the surface of this planet?

Two spherical bodies in the diagram have the same radius but the left mass has twice the mass of the other body. At which point could the net gravitational field of the two masses have the greatest magnitude?

A horizontal disc of radius $\mathit{45}\mathit{ }cm$ rotates about a vertical axis through its center. The disc makes one full revolution in $1.40 \mathrm{s}$ .A particle of mass 0.054 kg is placed at a distance from the centre of the disc. The particle does not move relative to the disc. On a copy of the diagram draw arrows to represent the velocity and acceleration of the particle.

A horizontal disc of radius $\mathit{45}\mathit{ }cm$ rotates about a vertical axis through its center. The disc makes one full revolution in $1.40 \mathrm{s}$ .A particle of mass $0.054 kg$ is placed at a distance $22 cm$ from the centre of the disc. The particle does not move relative to the disc. Calculate the angular speed an linear speed of the particle.

A horizontal disc of radius $\mathit{45}\mathit{ }cm$ rotates about a vertical axis through its center. The disc makes one full revolution in $1.40 \mathrm{s}$ .A particle of mass $0.054 kg$ is placed at a distance$22 cm$ from the centre of the disc. The particle does not move relative to the disc. The coefficient of static friction between the disc and the particle $0.82$ .Determine the largest distance (in meters) from the centre of disc where the particle can be placed and still not move relative to the disc.

A horizontal disc of radius $\mathit{45}\mathit{ }cm$ rotates about a vertical axis through its center. The disc makes one full revolution in $1.40 \mathrm{s}$ .A particle of mass $0.054 kg$ is placed at a distance$22 cm$ from the centre of the disc. The particle does not move relative to the disc. The particle is to maintain the original distance $22 \mathrm{cm}$ from the center of the disc.Determine the maximum angular velocity (in radian per second) of the disc so that the particle does not move relative to the disc.The coefficient of static friction is $0.82$.