JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
In an experiment to find acceleration due to gravity \((g)\) using simple pendulum, time period of \(0.5\,s\) is measured from time of \(100\) oscillation with a watch of \(1\;s\) resolution. If measured value of length is \(10\; cm\) known to \(1\; mm\) accuracy. The accuracy in the determination of \(g\) is found to be \(x \%\). The value of \(x\) is
- A \(4\)
- B \(5\)
- C \(3\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
\(T=2 \pi \sqrt{\frac{\ell}{g}}\) \(g=\frac{1}{4 \pi^{2}} \frac{T^{2}}{\ell}\) \(\frac{\Delta g}{g}=\frac{2 \Delta T }{ T }+\frac{\Delta \ell}{\ell}\) \(\frac{\Delta g}{g}=2 \cdot \frac{1}{100 \times 0.5}+\frac{1\,mm }{10\,cm }\) \(\frac{\Delta g}{g}=\frac{5}{100}\)
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
- For ac circuit shown in figure, \(\mathrm{R}=100 \mathrm{k} \Omega\) and \(\mathrm{C}=100 \mathrm{pF}\) and the phase difference between \(\mathrm{V}_{\text {in }}\) and \(\left(V_B-V_A\right)\) is \(90^{\circ}\). The input signal frequency is \(10^x \mathrm{rad} / \mathrm{sec}\), where ' x ' is ______.
JEE Mains 2025 Hard - An alternating current is given by \(\mathrm{I}=\mathrm{I}_{\mathrm{A}} \sin \omega \mathrm{t}+\mathrm{I}_{\mathrm{B}} \cos \omega \mathrm{t}\). The r.m.s current will be ______.JEE Mains 2025 Easy
- A heavy iron bar, of weight \(\mathrm{W}\) is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle \(\theta\) with the horizontal. The weight experienced by the person is _______.JEE Mains 2024 Hard
- The reverse breakdown voltage of a Zener diode is \(5.6\, V\) in the given circuit. The current \(I_z\) through the Zener is......\(mA\)
JEE Mains 2019 Hard - A proton (mass \(m\) ) accelerated by a potential difference \(V\) flies through a uniform transverse magnetic field \(B.\) The field occupies a region of space by width \('d'\). If \(\alpha \) be the angle of deviation of proton from initial direction of motion (see figure), the value of \(sin\,\alpha \) will be
JEE Mains 2015 Hard - A particle of mass \(m\) is moving along a trajectory given by
\(x = x_0 + a\, cos\,\omega_1 t\)
\(y = y_0 + b\, sin\,\omega_2t\)
The torque, acing on the particle about the origin, at \(t = 0\) isJEE Mains 2019 Hard
More PYQs from JEE Mains
- The series of positive multiples of \(3\) is divided into sets : \(\{3\},\{6,9,12\},\{15,18,21,24,27\}, \ldots\) Then the sum of the elements in the \(11^{\text {th }}\) set is equal to \(................\)JEE Mains 2022 Hard
- In a dilute gas at pressure \(P\) and temperature \(T\), the mean time between successive collisions of a molecule varies with \(T\) asJEE Mains 2020 Medium
- The area of the region in the first quadrant inside the circle \(x^2+y^2=8\) and outside the parabola \(\mathrm{y}^2=2 \mathrm{x}\) is equal to :JEE Mains 2024 Hard
- A square shaped coil of area \(70\,cm ^2\) having \(600\) turns rotates in a magnetic field of \(0.4\,wbm ^{-2}\), about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes \(500\) revolution in a minute, the instantaneous emf when the plane of the coil is inclined at \(60^{\circ}\) with the field, will be \(..........V\). (Take \(\pi=\frac{22}{7}\) )JEE Mains 2023 Medium
- A moving coil galvanometer of resistance \(100 \Omega\) shows a full scale deflection for a current of 1 mA . The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of 5 mA , is _________ \(\Omega\)JEE Mains 2026 Easy
- In the given figure, a mass \(M\) is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is \(k\). The mass oscillates on a frictionless surface with time period \(T\) and amplitude \(A\). When the mass is in equilibrium position, as shown in the figure, another mass \(m\) is gently fixed upon it. The new amplitude of oscillation will be
JEE Mains 2021 Medium