JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
In the given figure, two wheels \(P\) and \(Q\) are connected by a belt \(B\). The radius of \(P\) is three times as that of \(Q\). In case of same rotational kinetic energy, the ratio of rotational inertias \(\left(\frac{{I}_{1}}{{I}_{2}}\right)\) will be \({x}: 1\). The value of \({x}\) will be \(.....\, .\)
- A \(91\)
- B \(81\)
- C \(9\)
- D \(3\)
Answer & Solution
Correct Answer
(C) \(9\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{2} I_{1}\left(\omega_{1}\right)^{2}=\frac{1}{2} I_{2}\left(\omega_{2}\right)^{2}\) \(I_{1}\left(\frac{V}{3 R}\right)^{2}=I_{2}\left(\frac{v}{R}\right)^{2}\) \(\frac{I_{1}}{I_{2}}=\frac{9}{1}\)
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 metal plate of area \(1\times10^{-4}\, m^2\) is illuminated by a radiation of intensity \(16\, m\,W/m^2\). The work function of the metal is \(5\,eV\). The energy of the incident photons is \(10\, eV\) and only \(10\%\) of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be : \([1\, eV = 1.6\times10^{-19}\, J]\)JEE Mains 2019 Hard
- Two radioactive substances A and B of mass numbers \(200\) and \(212\) respectively, shows spontaneous \(\alpha\)-decay with same \(Q\) value of \(1\) MeV. The ratio of energies of \(\alpha\)-rays produced by A and B is ________.JEE Mains 2026 Medium
- Given below are two statement : Statement \(I :\) If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double. Statement \(II :\) Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio: In the light of the above statement, choose the correct answer from the options given below :JEE Mains 2023 Medium
- A LCR series circuit driven with \(E_{rms} = 90\) V at frequency \(f_d = 30\) Hz has resistance \(R = 80\,\Omega\), an inductance with inductive reactance \(X_L = 20.0\,\Omega\) and capacitance with capacitive reactance \(X_C = 80.0\,\Omega\). The power factor of the circuit is _______.JEE Mains 2026 Medium
- A small bob A of mass m is attached to a massless rigid rod of length 1m pivoted at point P and kept at an angle of \( 60^{\circ} \) with vertical as shown in figure. At distance of 1m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends to a circular track of radius R as shown in figure. If bob B just manages to complete the circular path of radius R upto a point Q after being hit elastically by both A, then radius R is ___________m.
JEE Mains 2026 Hard - A uniform chain of length \(3\, meter\) and mass \(3\, {kg}\) overhangs a smooth table with \(2\, meter\) laying on the table. If \(k\) is the kinetic energy of the chain in joule as it completely slips off the table, then the value of \({k}\) is (Take \(\left.g=10\, {m} / {s}^{2}\right)\)JEE Mains 2021 Hard
More PYQs from JEE Mains
- Let \( \frac{\pi}{2}<\theta<\pi \) and \( cot\theta=-\frac{1}{2\sqrt{2}} \). Then the value of \( sin(\frac{15\theta}{2})(cos8\theta+sin8\theta)+cos(\frac{15\theta}{2})(cos8\theta-sin8\theta) \) is equal to:JEE Mains 2026 Easy
- The general solution of the differential equation, \(\sin \,2x\,\left( {\frac{{dy}}{{dx}} - \sqrt {\tan \,x} } \right) - y = 0,\) isJEE Mains 2014 Hard
- Let the product of \(\omega_1=(8+i) \sin \theta+(7+4 i) \cos \theta\) and \(\omega_2=(1+8 i) \sin \theta+(4+7 i) \cos \theta\) be \(\alpha+i \beta\), \(\mathrm{i}=\sqrt{-1}\). Let p and q be the maximum and the minimum values of \(\alpha+\beta\) respectively.JEE Mains 2025 Medium
- The magnetic field of a plane electromagnetic Wave is \(\overrightarrow{ B }=3 \times 10^{-8} \sin [200 \pi( y + ct )] \hat{ i }\, T\) Where \(c=3 \times 10^{8} \,ms ^{-1}\) is the speed of light. The corresponding electric field isJEE Mains 2020 Hard
- When a resistance of \(5\,\Omega\) is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of \(250\,mA\), however when \(1050\,\Omega\) resistance is connected with it in series, it gives full scale deflection for \(25\) volt. The resistance of galvanometer is \(......\,\Omega\).JEE Mains 2023 Hard
- If the function \( f(x) = \frac{e^{x}(e^{\tan x-x}-1)+\log_{e}(\sec x+\tan x)-x}{\tan x-x} \) is continuous at \( x=0 \), then the value of \( f(0) \) is equal toJEE Mains 2026 Hard