A student records the initial length l, change in temperature and… - Vidyadip

Question

A student records the initial length l, change in temperature $\Delta\text{T}$ and change in length $\Delta\text{l}$ of a rod as follows:

S.NO.	l(m)	$\Delta\text{T(C)}$	$\Delta\text{l}(\text{m})$
1.	2	10	$4 \times 10^{-4}$
2.	1	10	$4 \times 10^{-4}$
3.	2	20	$2 \times 10^{-4}$
4.	3	10	$6 \times 10^{-4}$

If the first observation is correct, what can you say about observations 2, 3 and 4.

✓

Answer

If the first observation is correct, hence from the $1^{st}$ observation we get the coefficient of linear expansion. $\alpha=\frac{\Delta\text{l}}{\text{l}\times\Delta\text{T}}=\frac{4\times10^{-4}}{2\times10}=2\times10^{-5}{^\circ{\text{C}}^{-1}}$ For $2^{nd}$ observation, $\Delta\text{l}=\alpha\text{l}\Delta\text{T}$
$=2\times10^{-5}\times1\times10$
$=2\times10^{-4}\text{m}\neq4\times10^{-4}\text{m}$ Which is incorrect, For $3^{rd}$ observation, $\Delta\text{l}=\alpha\text{l}\Delta\text{T}$
$=2\times10^{-5}\times2\times20$
$=8\times10^{-4}\text{m}\neq2\times10^{-4}\text{m}$ which is incorrect. For $4^{th}$ observation, $\Delta\text{l}=\alpha\text{l}\Delta\text{T}$
$=2\times10^{-5}\times3\times10=6\times10^{-4}\text{m}$ [i.e., observed value is correct]

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Thermal Properties of Matter→Thermal Properties of Matter — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Prove that gravitational potential difference is the work done in carrying a unit mass from one point to another.

Two simple harmonic motions are represented by the following equations:$\text{y}_1=10\sin\frac{\pi}{4}(12\text{t}+1)$
and $\text{y}_2=5(\sin3\pi\text{t}+\sqrt{3}\cos\pi\text{t}).$ What is the ratio of their amplitudes?

Draw the following graphs for an object projected upward with a velocity $v _0$, which comes back to the same point after some time:
i. Acceleration versus time graph,
ii. Speed versus time graph,
iii. Velocity versus time graph.

A small body tied to one end of the string is whirled in a vertical circle. Represent the forces on a diagram when the string makes an angle $\theta$ with initial position below the fixed point. Find an expression for the tension in the string. Also, find the tension and velocity at the lowest and highest points respectively.

Taking the moon's orbit around earth to be r and mass of earth 81 times the mass of the moon. Find the position of the point from the earth, where the net gravitational field is zero.

Explain the Doppler's effect.

Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity): The mass of an elephant.

The position of a particle is given by $\vec{\text{r}}=9\text{t}\hat{\text{i}}+6\text{t}^2\hat{\text{j}}+8\hat{\text{k}},$ where $t$ is in seconds and the coefficients have the proper units for $\vec{\text{r}}$ to be in metres.

Find velocity $\vec{\text{v}}(\text{t})$ of particle and $\vec{\text{a}}(\text{t})$ acceleration of the particle.
Find the magnitude and direction of $\vec{\text{v}}(\text{t})$ at $t = 2sec.$

Compare the velocities of sound in hydrogen $\left( H _2\right)$ and carbon dioxide $\left( CO _2\right)$. The ratio $(\gamma)$ of specific heats of $H _2$ and $CO _2$ are respectively $1.4$ and $1.3 .$

Find the average velocity of a projectile between the instants it crosses half the maximum height. It is projected with a speed u at an angle $\theta$ with the horizontal.