An astronaut is orbiting Earth in a spaceship. Why does the astronaut experience weightlessness?

A.  The astronaut is outside the gravitational field of Earth.

B.  The acceleration of the astronaut is the same as the acceleration of the spaceship.

C.  The spaceship is travelling at a high speed tangentially to the orbit.

D.  The gravitational field is zero at that point.

A mass m attached to a string of length R moves in a vertical circle with a constant speed. The tension in the string at the top of the circle is T. What is the kinetic energy of the mass at the top of the circle?

A.   $\frac{R\left(T+mg\right)}{2}$

B.   $\frac{R\left(T-mg\right)}{2}$

C.   $\frac{Rmg}{2}$

D.   $\frac{R\left(2T+mg\right)}{2}$

P and Q are two moons of equal densities orbiting a planet. The orbital radius of P is twice the orbital radius of Q. The volume of P is half that of Q. The force exerted by the planet on P is F. What is the force exerted by the planet on Q?

A.  F

B.  2F

C.  4F

D.  8F

A small ball of weight W is attached to a string and moves in a vertical circle of radius R.

What is the smallest kinetic energy of the ball at position X for the ball to maintain the circular motion with radius R?

A.  $\frac{WR}{2}$

B.  W R

C.  2 W R

D.  $\frac{5WR}{2}$

Two satellites W and X have the same mass. They have circular orbits around the same planet. W is closer to the surface than X. What quantity is smaller for W than for X?

A.  Gravitational force from the planet

B.  Angular velocity

C.  Orbital speed

D.  Orbital period

The centre of the Earth is separated from the centre of the Moon by a distance D. Point P lies on a line joining the centre of the Earth and the centre of the Moon, a distance X from the centre of the Earth. The gravitational field strength at P is zero.

What is the ratio $\frac{\text{mass of the Moon}}{\text{mass of the Earth}}$?

A.  $\frac{{\left(D-X\right)}^2}{X^2}$

B.  $\frac{\left(D-X\right)}{X}$

C.  $\frac{X^2}{{\left(D-X\right)}^2}$

D.  $\frac{X}{D-X}$

An object of mass m moves in a horizontal circle of radius r with a constant speed v. What is the rate at which work is done by the centripetal force?

A.     $\frac{m{v}^3}{r}$

B.     $\frac{m{v}^3}{2\pi r}$

C.     $\frac{m{v}^3}{4\pi r}$

D.     zero