Question

It is observed that the value of acceleration due to gravity ' $g$ ' at a place is $980 {cm} / {sec}^{2}$; obtain its value in a system in which metre is the unit of length and minute is the unit of time.

Answer 1

Ans : $35280 .$

Solution : Since the dimension of $g=\left[\mathrm{LT}^{-2}\right]$

$\mathbf{N}_{2}=\mathbf{N}_{1}\left[\frac{\mathrm{U}_{1}}{\mathrm{U}_{2}}\right]$

=$\mathrm{N}_{1}\left[\frac{\mathrm{L}_{1}}{\mathrm{~L}_{2}}\right]\left[\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right]^{-2}$

=$\mathrm{N}_{1}\left[\frac{10^{-2} \mathrm{~m}}{\mathrm{~m}}\right]\left[\frac{1 / 60 \text { minute }}{\text { minute }}\right]^{-2}$

=$980 \times \frac{1}{100} \times 60^{2}=35280$ .