Question

Find dimension of d²Y ÷dx²
where Y = force & x = momentum.​

Answer 1

Dimension of $\frac{d²Y}{dx²}$

Dimension of $\frac{Y}{x²}$

Y = Force

X = momentum

Dimensional formula for Force is

$ml {t}^{ - 2}$

Dimensional formula for momentum is

$ML {T}^{ - 1}$

So,

$\frac{Y}{ {x}^{2} } = \frac{ML{T}^{ -2} }{ {(ML{T}^{ - 1}) }^{2} } \\ \\ = \frac{ML {T}^{ - 2} }{ {M}^{2} {L}^{2} {T}^{ - 2} } \\ \\ = {M}^{1} {M}^{ - 2} \: {L}^{1} {L}^{ - 2} \: {T}^{ - 2} {T}^{2} \\ \\ = {M}^{ - 1} {L}^{ - 1} {T}^{0}$

So, the dimension is

${M}^{ - 1} {L}^{ - 1} {T}^{0}$

Answer 2

Answer

$m {}^{ - 1} {l}^{ - 1} {t}^{0}$