Question

Dimension formula of force , work , torque​

Answer 1

Force = Mass × acceleration

F = m × a

Dimesion of mass = [ M ]

Dimension of a = [ L T^-2 ]

Dimesion of force

= [ M ] × [ L T^-2 ]

= [ M L T^-2 ]

Work = Force × displacement

Dimension of force = [ M L T^-2 ]

Dimension of displacement = [ L ]

Dimension of Work = [ M L T^-2 ] × [ L ]

= [ M L ^1+1 T^-2 ]

= [ M L ^2 T^-2 ]

Torque = Force × Perpendicular distance

Dimesion of force = [ M L T^-2 ]

Dimension of perpendicular distance = [L]

Thus Dimension of Torque = Dimesion of Work = [ M L ^2 T^-2 ]