Find the dimensional formula of Universal Gravitational Constant $G$, Planck's constant $h$, and Coefficient of viscosity $\eta$.
2.
By method of dimensions, derive the formula for time period $T$ of a simple pendulum assuming it depends on mass $m$, length $l$, and acceleration due to gravity $g$.
Section B: Error Analysis & Propagation
3.
The percentage errors in measurement of mass and speed are $2\%$ and $3\%$ respectively. Estimate max percentage error in kinetic energy.
4.
A physical quantity $P = \frac{A^3 B^2}{\sqrt{C} D}$. If percentage errors in $A, B, C, D$ are $1\%, 3\%, 4\%, 2\%$, find percentage error in $P$.
State rules for significant figures and find the number of significant figures in $0.007020\text{ m}^2$ and $6.022 \times 10^{23}$.
6.
A Vernier Calliper has 10 divisions on Vernier scale matching 9 divisions on Main scale ($1\text{ MSD} = 1\text{ mm}$). Find least count and measured length if main scale reading is $2.8\text{ cm}$ and 4th Vernier division coincides.
