Circular Motion & Gravitation Questionbank

An ion follows a circular path in a uniform magnetic field. Which single change decreases the radius of the path?

A projectile is fired from level ground with speed $v$ at an angle $heta$ to the ground. Ignoring air resistance, which of the following is a correct expression for the maximum height reached by the projectile?

A stone is thrown at an angle to the horizontal. Ignoring air resistance, the horizontal component of the initial velocity of the stone determines the value of

A motorcyclist is cornering on a curved race track.

Which combination of changes of banking angle $\theta$ and coefficient of friction $\mu$ between the tyres and road allows the motorcyclist to travel around the corner at greater speed?

Planet $X$ has a gravitational field strength of $18 \mathrm{Nkg}^{-1}$ at its surface. Planet $Y$ has the same density as $X$ but three times the radius of $X$. What is the gravitational field strength at the surface of $Y$?

Two satellites of equal mass, $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$, orbit the Earth. $\mathrm{S}_{1}$ is orbiting at a distance $r$ from the Earth's centre at speed $v . \mathrm{S}_{2}$ orbits at a distance $2 r$ from the Earth's centre at speed $\frac{v}{\sqrt{2}}$. The ratio of the centripetal force on $\mathrm{S}_{1}$ to the centripetal force on $\mathrm{S}_{2}$ is

Two isolated spheres of masses $M$ and $m$ are held a distance $d$ apart, as shown below.

Mass $M$ is greater than mass $m$.

The gravitational field strength $g$ is measured on a line between the two masses. Which graph best shows the variation with distance $x$ from the larger sphere of the magnitude of the field strength $g$ ? The Earth's gravitational field is to be ignored.