Question
What are the units on each side of the equation GMm/x^2=mv^2/x
Answers
GPT 3.5
On the left-hand side of the equation, GMm/x^2, the units are:
- G is the gravitational constant, which has units of N(m/kg)^2.
- M and m are the masses, which have units of kg.
- x is the distance, which has units of m.
Therefore, the left-hand side has units of N.
On the right-hand side of the equation, mv^2/x, the units are:
- m is the mass, which has units of kg.
- v is the velocity, which has units of m/s.
- x is the distance, which has units of m.
Therefore, the right-hand side has units of N.
The units on both sides of the equation are the same, N, indicating that the equation is dimensionally consistent.
- G is the gravitational constant, which has units of N(m/kg)^2.
- M and m are the masses, which have units of kg.
- x is the distance, which has units of m.
Therefore, the left-hand side has units of N.
On the right-hand side of the equation, mv^2/x, the units are:
- m is the mass, which has units of kg.
- v is the velocity, which has units of m/s.
- x is the distance, which has units of m.
Therefore, the right-hand side has units of N.
The units on both sides of the equation are the same, N, indicating that the equation is dimensionally consistent.