JEE Mains · Physics · STD 11 - 5. work,energy,power and collision
A particle moving in the \(xy\) plane experiences a velocity dependent force \(\overrightarrow{ F }= k \left( v _{ y } \hat{ i }+ v _{ x } \hat{ j }\right),\) where \(v _{ x }\) and \(v _{ y }\) are the \(x\) and \(y\) components of its velocity \(\overrightarrow{ v } .\) If \(\overrightarrow{ a }\) be the acceleration of the particle, then which of the following statements is true for the particle\(?\)
- A quantity \(\overrightarrow{ v } \cdot \overrightarrow{ a }\) is constant in time.
- B kinetic energy of particle is constant in time.
- C quantity \(\overrightarrow{ v } \times \overrightarrow{ a }\) is constant in lime.
- D \(\overrightarrow{ F }\) arises due to a magnetic field.
Answer & Solution
Correct Answer
(C) quantity \(\overrightarrow{ v } \times \overrightarrow{ a }\) is constant in lime.
Step-by-step Solution
Detailed explanation
\(\frac{ dv _{ x }}{ dt }=\frac{ k }{ m } v _{ y }\) \(\frac{ dv _{ y }}{ dt }=\frac{ k }{ m } v _{ x }\) \(\frac{ d v_{ y }}{ dv _{ x }}=\frac{ v _{ x }}{ v _{ y }} \Rightarrow \int v _{ y } dv _{ y }=\int v _{ x } dv _{ x }\) \(v_{y}^{2}=v_{x}^{2}+C\)…
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 output \(\mathrm{Y}\) of following circuit for given inputs is _______.
JEE Mains 2024 Hard - Ship \(A\) is sailing towards north -east with velocity \(\vec v = 30\,\hat i + 50\hat j\,km/hr\) where \(\hat i\) points east and \(\hat j\) , north. Ship \(B\) is at a distance of \(80\, km\) east and \(150\, km\) north of Ship \(A\) and is sailing towards west at \(10\, km/hr\). \(A\) will be at minimum distance from \(B\) is.........\(hrs\)JEE Mains 2019 Hard
- An electric appliance supplies \(6000\, {J} / {min}\) heat to the system. If the system delivers a power of \(90\, {W}\). How long (in \(sec\)) it would take to increase the internal energy by \(2.5 \times 10^{3}\, {J}\) ?JEE Mains 2021 Medium
- An electron of mass ' m ' with an initial velocity \(\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{i}\left(\mathrm{v}_0\gt0\right)\) enters an electric field \(\overrightarrow{\mathrm{E}}=-\mathrm{E}_{\mathrm{o}} \hat{\mathrm{k}}\). If the initial de Broglie wavelength is \(\lambda_0\), the value after time t would be _______.JEE Mains 2025 Hard
- Due to presence of an em-wave whose electric component is given by \(\mathrm{E}=100 \sin (\omega \mathrm{t}-\mathrm{kx}) \mathrm{NC}^{-1}\), a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified asJEE Mains 2025 Medium
- The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength \(491\, nm\) is \(0.710\, V\). When the incident wavelength is changed to a new value, the stopping potential is \(1.43\, V\). The new wavelength is ....... \(nm.\)JEE Mains 2021 Medium
More PYQs from JEE Mains
- A light beam is described by \(E=800 \sin \omega\left(t-\frac{x}{c}\right)\) An electron is allowed to move normal to the propagation of light beam with a speed of \(3 \times 10^{7}\;{ms}^{-1}\). What is the maximum magnetic force exerted on the electron ?JEE Mains 2021 Medium
- A \(\sqrt{34}\,m\) long ladder weighing \(10\,kg\) leans on a frictionless wall. Its feet rest on the floor \(3\,m\) away from the wall as shown in the figure. If \(F_{f}\) and \(F_{w}\) are the reaction forces of the floor and the wall, then ratio of \(F _{ a } / F _{f}\) will be: (Use \(\left.g=10\,m / s ^{2}\right)\)
JEE Mains 2022 Hard - When a rubber-band is stretched by a distance \(x\), it exerts restoring force of magnitude \(F=ax+bx^2\) where \(a\) and \(b\) areconstants. The work done in stretching the unstretched rubber-band by \(L\) isJEE Mains 2014 Medium
- If \(L=\sin ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right)\) and \(M=\cos ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right),\) thenJEE Mains 2020 Hard
- If the number of terms in the expansion of \({\left( {1 - \frac{2}{x} + \frac{4}{{{x^2}}}} \right)^n},x \ne 0\) is \(28\) then the sum of the coefficients of all the terms in this expansion, is :JEE Mains 2016 Hard
- 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