## Exam-Style Questions on Standard Form## Problems on Standard Form adapted from questions set in previous exams. |

## 1. | GCSE Higher |

The surface gravity, \(g\), of a planet is the gravitational acceleration experienced at its surface. The following formula can be used to find how a planet's gravity compares to Earth's.

$$g=\frac{6.67 \times 10^{-11} \times m}{r^2}$$Where \(m\) is the mass of the planet and \(r\) is the radius.

Find the ratio of the surface gravity on Jupiter and the surface gravity Mars. Give your answer in the form \(n:1\).

Mass (kg) | Radius (m) | |

Jupiter | 1.90 × 10^{27} | 6.68 × 10^{7} |

Mars | 6.39 × 10^{23} | 3.39 × 10^{6} |

## 2. | IB Studies |

The Moon appears to orbit around the Earth with an average radius of 385 thousand kilometres.

(a) Write down this radius, in kilometres, in the form \(a\times 10^k\), where \( 1\le a\lt 10,k\in \mathbb Z\)

(b) Calculate the distance, in kilometres, the Moon travels around the Earth in one orbit, assuming that the orbit is a circle.

It takes approximately 27.3 days for the Moon to complete one orbit.

(c) Calculate the total distance the Moon appears to travel around the earth during a leap year.

## 3. | GCSE Higher |

The volume of the Moon is \(2.2 \times 10^{10}\) km^{3}

The volume of the Saturn is \(8.3 \times 10^{14}\) km^{3}

How many times larger is the radius of Saturn than the radius of the Moon?

Assume that Saturn and the Moon are both spheres and that the volume \(v\) of a sphere with radius \(r\) is given by the following formula.

$$v=\frac43\pi r^3$$Give your answer to 2 significant figures.

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