JEE Mains · Physics · STD 11 - 3.2 motion in plane
A particle is moving with constant speed in a circular path. When the particle turns by an angle \(90^{\circ}\), the ratio of instantaneous velocity to its average velocity is \(\pi: x \sqrt{2}\). The value of \(x\) will be \(.........\)
- A \(2\)
- B \(5\)
- C \(1\)
- D \(7\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
Let instantaneous velocity be v. time, \(t =\frac{\text { Arc length }}{ v }=\frac{2 \pi \frac{ R }{4}}{ v }=\frac{\pi R }{2 v }\) average velocity, \(\langle v \rangle =\frac{ AB }{ t }=\frac{ R \sqrt{2}(2 v )}{\pi R }=\frac{2 \sqrt{2} V }{\pi}\)…
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
- A body of mass \((5 \pm 0.5) kg\) is moving with a velocity of \((20 \pm 0.4) m / s\). Its kinetic energy will beJEE Mains 2023 Medium
- A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point \(P\) which lies on the centre of the semicircle ?
JEE Mains 2021 Hard - The co-ordinates of a particle moving in \(x-y\) plane are given by : \(\mathrm{x}=2+4 \mathrm{t}, \mathrm{y}=3 \mathrm{t}+8 \mathrm{t}^2 .\) The motion of the particle is _______.JEE Mains 2024 Hard
- A short bar magnet is placed in the magnetic meridian of the earth with north pole pointing north . Neutral points are found at a distance of \(30\, cm\) from the magnet on the East - West line, drawn through the middle point of the magnet. The magnetic moment of the magnet in \(Am^2\) is close to: (Given \(\frac{{{\mu _0}}}{{4\pi }}\, = 10^{- 7}\) in \(SI\,units\) and \(B_H\, =\) Horizontal component field \(= 3.6\times10^{-5}\, tesla\))JEE Mains 2015 Medium
- A current of 5A exists in a square loop of side \(\frac{1}{\sqrt{2}} \mathrm{~m}\). Then the magnitude of the magnetic field \(B\) at the centre of the square loop will be \(p \times 10^{-6} \mathrm{~T}\). where, value of p is _____ .
\(\left[\right.\) Take \(\left.\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]\).JEE Mains 2025 Medium - A red \(LED\) emits light at \(0.1\) watt uniformly around it. The amplitude of the electric field of the light at a distance of \(1\ m\) from the diode is....\( Vm^{-1}\)JEE Mains 2015 Medium
More PYQs from JEE Mains
- Let \(H: \frac{-x^2}{a^2}+\frac{y^2}{b^2}=1\) be the hyperbola, whose eccentricity is \(\sqrt{3}\) and the length of the latus rectum is \(4 \sqrt{3}\). Suppose the point \((\alpha, 6), \alpha>0\) lies on \(H\). If \(\beta\) is the product of the focal distances of the point \((\alpha, 6)\), then \(\alpha^2+\beta\) is equal to :JEE Mains 2024 Hard
- Four fair dice are thrown independently \(27\) times. Then the expected number of times, at least two dice show up a three or a five, isJEE Mains 2020 Hard
- If \(y=y(x)\) is the solution of the differential equation \(\frac{d y}{d x}+2 y=\sin (2 x), y(0)=\frac{3}{4}\), then \(\mathrm{y}\left(\frac{\pi}{8}\right)\) is equal to :JEE Mains 2024 Medium
- In a series LCR circuit, a resistor of \(300 \Omega\), a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ \(\times 10^4\) radians \(\mathrm{s}^{-1}\).JEE Mains 2025 Medium
- An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are \(6.4 \;\mathrm{cm}\) and \(4.8 \;\mathrm{cm},\) respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is:JEE Mains 2020 Medium
- A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed \(v\). If \(x\) is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to \(x^\alpha\), where \(\alpha\) is _____.JEE Mains 2026 Hard