Practical Physics: NEET PYQs and weightage

Relative (percentage) error

Use it when: you want to compare how precise two readings are, e.g. $\pm 0.01\text{g}$ on $1.02\text{g}$ is $\pm 1\%$ but on $9.89\text{g}$ only $\pm 0.1\%$

Error in a product

Use it when: area or volume comes from measured sides, e.g. $0.6\%+1\%$ gives $1.6\%$ on $l\times b$

Sig figs in × and ÷

Keep as many significant figures as the input with the fewest.

Use it when: finding density, area or volume, e.g. $4.237\text{g}/2.51{\text{cm}}^3=1.69{\text{g cm}}^{-3}$

Sig figs in + and −

Keep as many decimal places as the input with the fewest.

Use it when: adding or subtracting readings, e.g. $436.32+227.2+0.301=663.8\text{g}$, and $12.9-7.06=5.8\text{g}$

Counting sig figs

All non-zero digits count, and zeros between them count. Leading zeros in a number below 1 do not count. Trailing zeros count only if there is a decimal point.

Use it when: a question asks how many sig figs, e.g. $0.06900$ has 4 and $123000$ has 3

Scientific notation

Every digit of $a$ is significant.

Use it when: a change of units creates trailing zeros, e.g. $4.700\text{m}=4.700\times 10^3\text{mm}$ still has 4 sig figs

Rounding off

A dropped digit above 5 raises the previous digit by 1, and below 5 leaves it unchanged. If the dropped digit is exactly 5, keep an even preceding digit and raise an odd one.

Use it when: rounding to 3 sig figs, e.g. $2.745\to 2.74$ but $2.735\to 2.74$

Order of magnitude

Use it when: estimating sizes, e.g. Earth's diameter $1.28\times 10^7\text{m}$ is of order $10^7\text{m}$

Plane and solid angle

Use it when: you need the units of plane angle (radian, rad) and solid angle (steradian, sr). Both angles are dimensionless.

Common dimensions

Use it when: checking or building any equation by dimensions

Principle of homogeneity

Every added or subtracted term must have the same dimensions as the left side.

Use it when: checking an equation, e.g. $x=x_0+v_{0}t+\frac{1}{2}a{t}^2$ has every term in $[\mathrm{L}]$

Dimensionless arguments

Whatever is inside $\sin$, $\cos$, $\log$ or $e^x$ must have no dimensions.

Use it when: finding the dimensions of constants hidden inside a function

Deriving a relation

Assume the first form and equate the powers of M, L and T to get the second.

Use it when: a quantity depends on up to three variables multiplied together. Note that $k$ can never be found by this method.

Changing units

A quantity with numerical value $n$ takes the new value when the new units are $\alpha$ kg, $\beta$ m and $\gamma$ s.

Use it when: converting into a new system, e.g. $1\text{cal}=4.2\text{J}=4.2{\alpha }^{-1}{\beta }^{-2}{\gamma }^2$ new units