Physics

# The length of a strip measured with a meter rod is 10.0 cm its width measured with a vernier caliper is 1.00 cm. The least count of the meter rod is 0.1 cm and that of vernier caliper caliper 0.01 cm water will be error in its area?

$\pm 2$%

##### SOLUTION

Given,

Least count of tape is $0.1\,cm$

Least count of Vernier caliper is $0.01\,cm$

Length, $L=10\,cm$

Width, $W=1\,cm$

$area$,$A=Length\times width=L\times W$

Take ln and differentiate,

$\dfrac{\Delta A}{A}=\dfrac{\Delta L}{L}+\dfrac{\Delta W}{W}$

$\dfrac{\Delta A}{A}=\dfrac{0.1}{10}+\dfrac{0.01}{1}=0.02=2\,percent\,$

Hence, error in area is $\pm2$ %

You're just one step away

Single Correct Medium Published on 18th 08, 2020
Questions 244531
Subjects 8
Chapters 125
Enrolled Students 197

#### Realted Questions

Q1 Single Correct Hard
The length $\ell$, breadth b and thickness t of a block of wood were measured with the help of a measuring scale. The results with permissible errors are $\ell$ = 15.12 $\pm$ 0.01 cm, t = 5.28 $\pm$ 0.01 cm. $b$ = 10.15 $\pm$ 0.01 cm. The percentage error in volume upto proper significant figures is :
• A. 0.28%
• B. 0.36%
• C. 0.48%
• D. 0.64%

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q2 Single Correct Hard
The viscosity of a gas depends on mass, the effective diameter and the mean speed of the molecules. At room temperature, for He, $\eta_{He}=2\times 10^{-5}$ $kg{m}^{-1}{s}^{-1}$ and for $CH_{4}$, $\eta _{CH_{4}}=1.1\times 10^{-5}kgm^{-1}s^{-1}$. The diameter of the He atom is $2.1\times 10^{-10}m$ . lf the diameter of  $CH_{4}$ is $n\times 10^{-10}m$, find $'n'$.
Given mean speed of the molecules of the gas $v\propto \sqrt{\frac{K_B T}{m}}$ , where $K_B$ is the boltzmann's constant , $T$ is temperature and m is the mass of the gas.
• A. $2.1$
• B. $4$
• C. $3.2$
• D. $3$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q3 Subjective Medium
Find the dimensions of G in the equation $F=\dfrac{Gm_{1}m_{2}}{r^{2}}$ ; where F is the force of gravitational attraction between two bodies of point masses $m_{1}$ and $m_{2}$ , 'r' is the distance of separation between them.

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q4 Subjective Hard
Assuming that mass (M) of the largest stone that can be moved by a flowing river depends upon the velocity (v) the density of water (p), and acceleration due to gravity (g). Using dimensional analysis show that M varies with the sixth power of the velocity of flow.

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q5 Single Correct Medium
1 $\mathring{A}$ is equal to :
• A. $0.1$ nm
• B. $10^{-10}$ cm
• C. $10^{-8} m$
• D. $10^{-4} \mu$.

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020