JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2021
- Hard
- Numerical
Three students \(S_{1}, S_{2}\) and \(S_{3}\) perform an experiment for determining the acceleration due to gravity \((g)\) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.
| Student No. | Length of pendulum \((cm)\) | No. of osci \((n)\) | Total time for osci | Time period \((s)\) |
| \(1.\) | \(64.0\) | \(8\) | \(128.0\) | \(16.0\) |
| \(2.\) | \(64.0\) | \(4\) | \(64.0\) | \(16.0\) |
| \(3.\) | \(20.0\) | \(4\) | \(36.0\) | \(9.0\) |
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
\(T=2 \pi \sqrt{\frac{\ell}{g}} \Rightarrow g=\frac{4 \pi^{2} \ell}{T^{2}}\)
\(\frac{\Delta g}{g}=\frac{\Delta \ell}{\ell}+\frac{2 \Delta T}{T}\)
\(\Delta T=\frac{\text { least count of time }\left(\Delta T_{0}\right)}{\text { number of oscillations(n) }}\)
\(\frac{\Delta g}{g}=\frac{\Delta \ell}{\ell}+\frac{2 \Delta T_{0}}{n T}\)
As \(\Delta \ell\) and \(\Delta T_{0}\) same for all observations so \(\frac{\Delta g}{g}\) is minimum for highest value of,\(n\) and \(T\)
Minimum percentage error in \(g\) is for student number\(-1\)
More questions from Physics
- In the figure shown, a circuit contains two identical resistors with resistance \(R = 5\,\Omega \) and an inductance with \(L = 2\, mH\). An ideal battery of \(15\, V\) is connected in the circuit. What will be the current through the battery long after the switch is closed?......\(A\)
JEE Mains 2019 Medium - A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area \('a'\) is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is \((a\,<\,<\,A)\)
JEE Mains 2021 Hard - An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii \(r_e,r_p\) and \({r_\alpha }\) respectively in a uniform magnetic field \(B\). The relation between \(r_e,r_p\) and \(\;{r_\alpha }\) isJEE Mains 2018 Medium
- The position of a particle related to time is given by \(x =\left(5 t ^2-4 t +5\right) m\). The magnitude of velocity of the particle at \(t=2\,s\) will be \(...........ms^{-1}\)JEE Mains 2023 Easy
- A fly wheel is accelerated uniformly from rest and rotates through \(5 \,rad\) in the first second. The angle rotated by the fly wheel in the next second, will be.........\(rad\)JEE Mains 2022 Easy
- Surface of certain metal is first illuminated with light of wavelength \({\lambda _1} = 350\,nm\) and then, the light of wavelength \({\lambda _2} = 540\,nm\). It is found that the maximum speed of the photo electrons in the two cases differ by a factor of \(2\). The work function of the metal (in \(eV\)) is close to: (Energy of photon \( = \frac{{1240}}{{\lambda {\rm{(in\, nm)}}}}\,eV\))JEE Mains 2019 Hard
More PYQs from JEE Mains
- Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of \(T\). The total internal energy, \(U\) of a mole of this gas, and the value of \(\gamma\left(=\frac{ C _{ P }}{ C _{ v }}\right)\) given, respectively, byJEE Mains 2020 Medium
- A transparent block A having refractive index \(\mu=1.25\) is surrounded by another medium of refractive index \(\mu=1.0\) as shown in figure. A light ray is incident on the flat face of the block with incident angle \(\theta\) as shown in figure. What is the maximum value of \(\theta\) for which light suffers total internal reflection at the top surface of the block?
JEE Mains 2025 Medium - For equal point charges \(Q\) each are placed in the \(xy\) plane at \((0, 2), (4, 2), (4, -2)\) and \((0, -2)\). The work required to put a fifth change \(Q\) at the origin of the coordinate system will beJEE Mains 2019 Hard
- A plane electromagnetic wave of frequency \(25\; \mathrm{GHz}\) is propagating in vacuum along the \(z-\)direction. At a particular point in space and time, the magnetic field is given by \(\overrightarrow{\mathrm{B}}=5 \times 10^{-8} \hat{\mathrm{j}}\; \mathrm{T}\). The corresponding electric field \(\overrightarrow{\mathrm{E}}\) is (speed of light \(\mathrm{c}=3 \times 10^{8}\; \mathrm{ms}^{-1})\)JEE Mains 2020 Easy