JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2021
- Hard
- Numerical
The diameter of a spherical bob is measured using a vernier callipers. \(9\) divisions of the main scale, in the vernier callipers, are equal to \(10\) divisions of vernier scale. One main scale division is \(1\, {mm}\). The main scale reading is \(10\, {mm}\) and \(8^{\text {th }}\) division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of \(0.04\, {cm}\), then the radius of the bob is \(...... \,\times 10^{-2} \,{cm}\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(52\)
Step-by-step Solution
Detailed explanation
\(9 \,{MSD}=10 \,{VSD}\)
\(9 \times 1\, {mm}=10\, {VSD}\)
\(\therefore 1 \,{VSD}=0.9\, {mm}\)
\({LC}=1\, {MSD}-1\, {VSD}=0.1 \,{mm}\)
Reading \(={MSR}+{VSR} \times {LC}\)
\(10+8 \times 0.1=10.8\, {mm}\)
Actual reading \(=10.8-0.4=10.4\, {mm}\)
radius \(=\frac{{d}}{2}=\frac{10.4}{2}=5.2 \,{mm}\)
\(=52 \times 10^{-2}\, {cm}\)
More questions from Physics
- A tennis ball (treated as hollow spherical shell) starting from \(O\) rolls down a hill. At point \(A\) the ball becomes air borne leaving at an angle of \(30^o\) with the horizontal. The ball strikes the ground at \(B\). What is the value of the distance \(AB\) ? (Moment of inertia of a spherical shell of mass \(m\) and radius \(R\) about its diameter .......... \(m\). \(= \frac {2}{3}\,mR^2\))
JEE Mains 2013 Hard - A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil is _______.(specific gravity of Kerosene oil \(=0.8\), specific gravity of ice \(=0.9\) )
JEE Mains 2024 Hard - If the deBroglie wavelength of an electron is equal to \(10^{-3}\) times the wavelength of a photon of frequency \(6\,\times 10^{14}\,Hz,\) then the speed of electron is equal to: (Speed of light \(=3\times 10^8\,m/s\,;\) Planck’s constant \(=6.63\times 10^{-34}\,J.s\,;\) Mass of electron \(=9.1\times 10^{-31}\,kg\) )JEE Mains 2019 Medium
- A ray of light passing through an equilateral prism is having velocity \(2.12 \times 10^8\) m/s in the prism material, then the minimum angle of deviation is _________ degrees.JEE Mains 2026 Medium
- In a Young's double slit experiment set up, the two slits are kept 0.4 mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness \(20 \mu m\) is introduced in front of one of the slits then centre bring fringe shifts by 20 mm on the screen. The refractive index of transparent sheet is given by \(\frac{\alpha}{10}\), where \(\alpha\) is _________ .JEE Mains 2026 Hard
- An expression for a dimensionless quantity \(P\) is given by \(P=\frac{\alpha}{\beta} \log _{e}\left(\frac{ kt }{\beta x }\right)\); where \(\alpha\) and \(\beta\) are constants, \(x\) is distance ; \(k\) is Boltzmann constant and \(t\) is the temperature. Then the dimensions of \(\alpha\) will beJEE Mains 2022 Medium
More PYQs from JEE Mains
- In hydrogen atom spectrum, (R is Rydberg's constant):
A. the maximum wavelength of the radiation of Lyman series is \(\frac{4}{3 R}\)
B. the Balmer series lies in the visible region of the spectrum
C. the minimum wavelength of the radiation of Paschen series is \(\frac{9}{R}\)
D. the minimum wavelength of Lyman series is \(\frac{5}{4 R}\)
Choose the correct answer from the options given below :JEE Mains 2026 Medium - An electron with mass ' \(m\) ' with an initial velocity \((\mathrm{t}=0) \overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\mathrm{i}} \quad\left(\mathrm{v}_0 \gt 0\right)\) enters a magnetic field \(\vec{B}=B_0 \hat{j}\). If the initial de-Broglie wavelength at \(\mathrm{t}=0\) is \(\lambda_0\) then its value after time ' t ' would be :JEE Mains 2025 Medium
- Two simple pendulums having lengths \(l_1\) and \(l_2\) with negligible string mass undergo angular displacements \(\theta_1\) and \(\theta_2\), from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?JEE Mains 2025 Medium
- A balloon has mass of \(10\,g\) in air. The air escapes from the balloon at a uniform rate with velocity \(4.5\,cm / s\). If the balloon shrinks in \(5\,s\) completely. Then, the average force acting on that balloon will be (in dyne).JEE Mains 2022 Easy
- A cricket player catches a ball of mass \(120 \mathrm{~g}\) moving with \(25 \mathrm{~m} / \mathrm{s}\) speed. If the catching process is completed in \(0.1 \mathrm{~s}\) then the magnitude of force exerted by the ball on the hand of player will be _______ (in SI unit).JEE Mains 2024 Easy