Embibe Experts Solutions for Chapter: Physical World and Measurement, Exercise 1: Exercise 1

Which of the following expressions has the same dimension as that of light-year? (In the following expressions, $h$ is Planck's constant, $c$ is the velocity of light and $G$ denotes Newton's gravitational constant.)

In an experiment to determine the acceleration due to gravity $g$, the formula used for the time period of a period of a periodic motion is, $T=2\pi \sqrt{\frac{7\left(R-r\right)}{5g}}$. The values of $R$ and $r$ are measured to be $\left(60\pm 1\right) \mathrm{mm}$ and $\left(10\pm 1\right) \mathrm{mm}$, respectively. In five successive measurements, the time period is found to be $0.52 \mathrm{s}\text{,} 0.56 \mathrm{s}\text{,} 0.57 \mathrm{s}\text{,} 0.54 \mathrm{s}$ and $0.59 \mathrm{s}$. The least count of the watch used for the measurement of time period is $0.01 \mathrm{s}$. Which of the following statement(s) is (are) true?

A drop of liquid of radius $\mathrm{r}$, density $\rho$ and surface tension $\sigma$ oscillates in gravity free space as shown in figure. If the time period of oscillation of this drop is $2$ sec, if the time period of oscillation of a drop of radius $2\mathrm{r}$ is $\sqrt{x} \mathrm{s}$. What is the value of $x$?

The second drop is made of same liquid as first.

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is $0.5 \mathrm{mm} \&$ there are $50$ divisions on the circular scale. The reading on the main scale is $2.5 \mathrm{mm} \&$ that on the circular scale is $20$ divisions. If the measured mass of the ball has a relative error of $2\%,$ the relative percentage error in the density is____(Approximate the answer to the nearest integer.)

Two capacitors with capacitance values ${\mathrm{C}}_1=2000\pm 10 \mathrm{pF}$ and ${\mathrm{C}}_2=3000\pm 15 \mathrm{pF}$ are connected in series. The voltage applied across this combination is $\mathrm{V}=5.00\pm 0.02 \mathrm{V}.$ The error in the calculation of the energy stored in this combination of capacitors is $\frac{n}{1000}$ then what is the value of $n$?

The kinetic energy of a particle depends on the square of speed of the particle. If error in measurement of speed is $30\%$, the error in the measurement of kinetic energy will be $n\%$. The value of $n$ is _____.

A wire has a mass $(0.3\pm 0.003)\mathrm{g}$, radius $(0.5\pm 0.005)\mathrm{mm}$ and length $(6\pm 0.06)\mathrm{cm}$. The maximum percentage error in measurement of density is $n$. The value of $n$ is _____.

If the length and breadth of a thin rectangular sheet are measured using a meter scale as $16.2 \mathrm{cm}$ and $10.1 \mathrm{cm}$ respectively, its surface area is $\left(164\pm x\right) {\mathrm{cm}}^2$. Then value of $x$ is,