Download App

JEE Main 28-Jan-2025 Paper - Shift 1 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 28-Jan-2025 Paper - Shift 14 Marks
Question
A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\frac{\mathrm{x}}{100}$ where x is $\qquad$
✓

Answer

(3)
Image
Since least count of the instrument can be calculated as
Least count $=\frac{\text { pitch length }}{\text { No. of division on circular scale }}$
$=\frac{0.75}{15}=0.05 \mathrm{~mm}$.
Here we are provided $\mathrm{L}=5 \mathrm{~mm} \& \mathrm{~W}=2.5 \mathrm{~mm}$
$\mathrm{L}=5 \mathrm{~mm} \& \mathrm{~W}=2.5 \mathrm{~mm}$
$\because$ We know that
A = L.W
For calculating fractional error, we can write
$\frac{\mathrm{dA}}{\mathrm{A}}=\frac{\mathrm{dL}}{\mathrm{L}}+\frac{\mathrm{dW}}{\mathrm{W}}$
Here $\mathrm{dL}=\mathrm{dW}=0.05 \mathrm{~mm}$
$\frac{\mathrm{dA}}{\mathrm{A}}=\frac{0.05}{5}+\frac{0.05}{2.5}$
$\Rightarrow \frac{\mathrm{dA}}{\mathrm{A}}=\frac{1}{100}+\frac{2}{100}=\frac{3}{100}$,
So, $x=3$

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 "SECTION - B [PHYSICS - NUMERIC]" from JEE Main 28-Jan-2025 Paper - Shift 1→JEE Main 28-Jan-2025 Paper - Shift 1 — all question types→JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The sound intensity level at a point $4 \,m$ from the point source is $10 \,dB$, then the sound level at a distance $2 \,m$ from the same source will be ........ $dB$
→
A charge $3$ coulomb experiences a force $3000$ $N$ when placed in a uniform electric field. The potential difference between two points separated by a distance of $1$ $cm$ along the field lines is.....$V$
→
A bomb of mass $9\, kg$ explodes into two pieces of masses $3\, kg$ and $6\, kg$. The velocity of mass $3\, kg$ is $16\, m/s$. The $KE$ of mass $6\, kg$ is ............ $\mathrm{J}$
→
Five equal forces of $10 \,N$ each are applied at one point and all are lying in one plane. If the angles between them are equal, the resultant force will be ........... $\mathrm{N}$
→
A current of $5$ $ampere$ is flowing in a wire of length $1.5$ $metres$. A force of $7.5\, N$ acts on it when it is placed in a uniform magnetic field of $2\, Tesla$. The angle between the magnetic field and the direction of the current is......$^o$
→
A body of mass $0.5 \,kg$ is projected under gravity with a speed of $98 \,m/s$ at an angle of ${30^o}$ with the horizontal. The change in momentum (in magnitude) of the body is ......... $N-s$
→
If a Second's pendulum is moved to a planet where acceleration due to gravity is $4$ times, the length of the second's pendulum on the planet should be made .......... times
→
A particle of mass $2 / 3 kg$ with velocity $v=-15 \,m / s$ at $t=-2 \,s$ is acted upon by a force $F=k-\beta t^{2}$. Here, $k=8 \,N$ and $\beta =2 \,N / s ^{2}$. The motion is one-dimensional. Then, the speed at which the particle acceleration is zero again, is ........... $m/s$
→
A proton carrying $1\, Me V$ kinetic energy is moving in a circular path of radius $R$ in uniform magnetic field. What should be the energy of an $\alpha -$ particle to describe a circle of same radius in the same field ?........$MeV$
→
A vertical U-tube of uniform cross-section contains water in both the arms. A $10 \,cm$ glycerine column ($R.D$. $=1.2$ ) is added to one of the limbs. The level difference between the two free surfaces in the two limbs will be ...... $cm$
→