COMEDK2014PhysicsUnits and Dimensions
The dimensions of universal gravitational constant is
Options
- A[ M ² ~L ³ ~T ⁻² ]
- B[ M ⁻¹ ~L ³ ~T ⁻² ]
- C[ M ⁻² ~L ³ ~T ⁻² ]
- D[ M ² ~L ⁻³ ~T ⁻² ]
Correct answer
B. [ M ⁻¹ ~L ³ ~T ⁻² ]
Step-by-step solution
According to Newton's law of gravitation, F= G m₁ m₂ r² where, F= force between two objects of masses m₁ and m₂ and r= distance between m₁ and m₂ . array ll & G= F r² m₁ m₂ & [ G ]= [ F ] [ r ² ] [ m ₁ ] [ m ₂ ] = [ MLT ⁻² ] [ L ² ] [ M ][ M ] = [ M ⁻¹ ~L ³ ~T ⁻² ] array