Question

If velocity , time and force were chosen as basic quantities , find the dimensions of mass and energy .

Answer 1

Velocity=distance/time    dimension of velocity=LT-1     Force=mass x accelaration   accelaration =velocity/time     dimension of accelaration=LT-1/T =LT-2                   Force=mass x accelaration    mass=force/accelaration   dimension of     mass=dimensionofforce/dimension of accelaration  =MLT-2/ LT-2=M                      DIMENSION OF MASS=M

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Answer 2

The dimensions of mass and energy as given below.

• Momentum=force × time
• m×v= force×time
• m=force×time×v⁻¹
• There for the dimension of m=[FTV⁻¹]
• Now the dimension of energy.
• The energy means the amount of work done .
• Therefore Work or energy= force ×displacement.
• Force dimension is [M¹L¹T⁻²]
• Therefore Energy=[M¹L²T⁻²] that is dimension.