1 Newton's gravitational constant, \(G\), is approximately \(6.67 \times 10 ^ { - 11 } \mathrm {~N} \mathrm {~m} ^ { 2 } \mathrm {~kg} ^ { - 2 }\).
- Find the dimensions of \(G\).
The escape velocity, \(v\), of a body from a planet's surface, is given by the formula \(\mathrm { v } = \mathrm { kG } ^ { \alpha } \mathrm { M } ^ { \beta } \mathrm { r } ^ { \gamma }\),
where \(M\) is the planet's mass, \(r\) is the planet's radius and \(k\) is a dimensionless constant. - Use dimensional analysis to find \(\alpha , \beta\) and \(\gamma\).