JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
The time period of a simple pendulum is given by \(T =2 \pi \sqrt{\frac{\ell}{ g }}\). The measured value of the length of pendulum is \(10\, cm\) known to a \(1\, mm\) accuracy. The time for \(200\) oscillations of the pendulum is found to be \(100\) second using a clock of \(1s\) resolution. The percentage accuracy in the determination of \('g'\) using this pendulum is \('x'\). The value of \('x'\) to the nearest integer is ...........\(\%\)
- A \(2\)
- B \(3\)
- C \(5\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\(g=\frac{4 \pi^{2} \ell}{T^{2}}\) \(\frac{\Delta g}{g}=\frac{\Delta \ell}{\ell}+2 \frac{\Delta T}{T}=\frac{0.1}{10}+2\left(\frac{\frac{1}{200}}{0.5}\right)\) \(\frac{\Delta g}{g}=\frac{1}{100}+\frac{1}{50}\) \(\frac{\Delta g}{g} \times 100=3 \%\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is __________ m/s.JEE Mains 2026 Medium
- As shown in figure, when a spherical cavity (centred at \(\mathrm{O})\) of radius \(1\) is cut out of a uniform sphere of radius \(\mathrm{R} \text { (centred at } \mathrm{C}),\) the centre of mass of remaining (shaded) part of sphere is at \(G\), i.e, on the surface of the cavity. \(\mathrm{R}\) can be detemined by the equation
JEE Mains 2020 Hard - In materials like aluminium and copper, the correct order of magnitude of various elastic modulii isJEE Mains 2014 Medium
- Choose the correct option from the following options given belowJEE Mains 2022 Medium
- Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is \(1: 4\), then \(A.\) The \(r.m.s\). velocity of gas molecules in two vessels will be the same. \(B.\) The ratio of pressure in these vessels will be \(1: 4\) \(C.\) The ratio of pressure will be \(1: 1\) \(D.\) The \(r.m.s.\) velocity of gas molecules in two vessels will be in the ratio of \(1: 4\)JEE Mains 2022 Medium
- A particle is executing simple harmonic motion \((SHM)\) of amplitude \(A,\) along the \(x-\) axis, about \(x = 0.\) When its potential energy \((PE)\) equals kinetic energy \((KE),\) the position of the particle will beJEE Mains 2019 Medium
More PYQs from JEE Mains
- Let \(A=I_2-2 \mathrm{MM}^{\mathrm{T}}\), where \(\mathrm{M}\) is real matrix of order \(2 \times 1\) such that the relation \(M^T M=I_1\) holds. If \(\lambda\) is a real number such that the relation \(\mathrm{AX}=\lambda \mathrm{X}\) holds for some non-zero real matrix \(X\) of order \(2 \times 1\), then the sum of squares of all possible values of \(\lambda\) is equal to :JEE Mains 2024 Hard
- A solid ball of radius \(R\) has a charge density \(\rho \) given by \(\rho = {\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(0 \leq r \leq R\). The electric field outside the ball isJEE Mains 2018 Hard
- Two discs have moments of intertia \({I}_{1}\) and \({I}_{2}\) about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, \(\omega_{1}\) and \(\omega_{2}\) respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :JEE Mains 2021 Hard
- A particle performs simple harmonic motion with amplitude \(A\). Its speed is trebled at the instant that it is at a distance \(\frac{{2A}}{3}\) from equilibrium position. The new amplitude of the motion isJEE Mains 2024 Hard
- Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by \(y=\left(10 \cos \pi x \sin \frac{2 \pi t}{T}\right)\, cm\) The amplitude of the particle at \(x =\frac{4}{3} \,cm\) will be........ \(cm\).JEE Mains 2022 Easy
- In a series \(LCR\) circuit, the inductance, capacitance and resistance are \(L =100\, mH , C =100 \mu F\) and \(R =\) \(10 \Omega\) respectively. They are connected to an \(AC\) source of voltage \(220\, V\) and frequency of \(50\, Hz\). The approximate value of current in the circuit will be.....\(A.\)
JEE Mains 2022 Medium