Question

Y=x^3sin(2πA/v),where x is the postion of particle and v is velocity,find the unit of Y/A^2

Answer 1

given expression, Y = x³sin(2πA/v)

where x is position of particle so, unit of x is metre or m .

here , unit of Y = unit of x³sin(2πA/v)

but we know, mathematical expressions has not units.

so, unit of sin(2πA/v) = nothing.

now unit of Y = unit of x³

= (unit of x)³ = m³

v is velocity so, unit of velocity is m/s .

we know,

phase (angle) of trigonometric is dimensionless quantity.

so, (2πA/v) is dimensionless quantity.

it is possible only when, dimension of A = dimension of v

so, dimension of A = dimension of v

or, unit of A = unit of v

hence, unit of A is m/s.

now we have to find unit of Y/A²

unit of Y/A² = unit of Y/unit of A²

= m³/(m/s)²

= m³/(m²/s²)

= ms²

hence, unit of Y/A² = ms²