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Units and Measurement
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Consider that $\sigma_s$, $k_B$, b represents Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of $\sigma_sk_B^{-1}b$ is$[\sigma_s][k_B^{-1}][b]=\left[\frac{Intensity}{(Temp)^4}\right]\left[\frac{Energy}{Temp}\right]^{-1}[\lambda_{max}\,Temp]=\left[\frac{MT^{-3}}{K^4}\right]\left[\frac{ML^2T^{-2}}{K}\right]^{-1}[LK]=[M^0L^{-1}T^{-1}K^{-2}]$.
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The physical quantity that has the same dimensional formula as pressure is:$[P]=\frac{[F]}{[A]}=\frac{MLT^{-2}}{L^2}=ML^{-1}T^{-2}$. Young's modulus $Y=\frac{stress}{strain}=\frac{F/A}{\Delta L/L}$ has the same dimensions $ML^{-1}T^{-2}$.
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The percentage error in the measurement of g is: (Given that $g=\frac{4\pi^2L}{T^2}$, $L=(10\pm0.1)$ cm, $T=(100\pm1)$ s)$\frac{\Delta g}{g}\times100=\frac{\Delta L}{L}\times100+2\frac{\Delta T}{T}\times100=\left(\frac{0.1}{10}\times100\right)+2\left(\frac{1}{100}\times100\right)=1+2=3\%$.
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The main scale of a vernier calliper has n divisions/cm. n divisions of the vernier scale coincide with (n-1) divisions of main scale. The least count of the vernier calliper is,$n\ VSD=(n-1)\ MSD \Rightarrow 1\ VSD=\frac{n-1}{n}$ MSD. LC $=1\ MSD-1\ VSD=\frac{1}{n}$ MSD $=\frac{1}{n}\times\frac{1}{n}$ cm $=\frac{1}{n^2}$ cm.