Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Measurements, Exercise 2: Critical Thinking

The force $F$ is expressed in terms of distance $x$ and time $t$ as $F=a\sqrt{x}+b{t}^2$. The dimensions of $\mathrm{a}/\mathrm{b}$ is

The error in the measurement of length $\left(L\right)$ of the simple pendulum is $0.1\%$ and the error in time period $\left(T\right)$is$3\%$. The maximum possible error in the measurement of $\frac{L}{T^2}$ is
 

The period of oscillation of a simple pendulum is given by $T=2\pi \sqrt{\frac{l}{g}}$ where $l$ is about $100 \mathrm{cm}$ and is known to have $1 \mathrm{mm}$ accuracy. The period is about $2 \mathrm{s}$. The time of $100$ oscillations is measured by a stopwatch of least count$0.1 \mathrm{s}$. The percentage error in $g$ is
 

The length, breadth and height of a rectangular block of wood were measured to be $\mathrm{l}=13.12\pm 0.02 \mathrm{cm}$, $\mathrm{b}=7.18\pm 0.01\mathrm{cm}$ and $h=4.16\pm 0.02 \mathrm{cm}$.
The percentage error in the volume of the block will be
 

The heat dissipated in a resistor can be determined from the relation: $H=\frac{I^{2}RT}{4.2} \mathrm{calory}$. If the maximum errors in the measurement of current $\left(I\right)$, resistance $\left(R\right)$ and time $\left(T\right)$ are $2 \%, 1\%$ and $1 \%$ respectively, what would be the maximum error in the dissipated heat?

If momentum $\left(P\right)$, area $\left(A\right)$ and time $\left(T\right)$ are assumed to be fundamental quantities, then energy has dimensional formula

Assertion: Avogadro number is the number of atoms in one gram mole.

Reason: Avogadro number is a dimensionless constant.

Assertion: The graph between $P$ and $Q$ is a straight line when $\frac{P}{Q}$ is constant.

Reason: The straight-line graph means that $P$ is proportional to $Q$ or $P$ is equal to constant multiplied by $Q$.