enEnglishguગુજરાતી
JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A ring of mass \(M\) and radius \(R\) is rotating about its axis with angular velocity \(\omega \). Two identical bodies each of mass \(m\) are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be
- A \(\frac{{m\left( {M + 2m} \right)}}{M}\,{\omega ^2}{R^2}\)
- B \(\frac{{Mm}}{{\left( {M + m} \right)}}\,{\omega ^2}{R^2}\)
- C \(\frac{{Mm}}{{\left( {M + 2m} \right)}}\,{\omega ^2}{R^2}\)
- D \(\frac{{\left( {M + m} \right)M}}{{\left( {M + 2m} \right)}}\,{\omega ^2}{R^2}\)
Answer & Solution
Correct Answer
(C) \(\frac{{Mm}}{{\left( {M + 2m} \right)}}\,{\omega ^2}{R^2}\)
Step-by-step Solution
Detailed explanation
\begin{array}{l} Kinetic\,energ{y_{\left( {rotational} \right)}}{K_R} = \frac{1}{2}I{\omega ^2}\\ kinetic\,energ{y_{(translational)}}{K_r} = \frac{1}{2}M{v^2}\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\…
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 force of \(- P \hat{k}\) acts on the origin of the coordinate system. The torque about the point \((2,-3)\) is \(P(a \hat{i}+b \hat{j})\), the ratio of \(\frac{a}{b}\) is \(\frac{x}{2}\). The value of \(x\) isJEE Mains 2023 Medium
- In the circuit shown in the figure, the total charge in \(750\, \mu C\) and the voltage across capacitor \(C _{2}\) is \(20\, V\). Then the charge on capacitor \(C _{2}\) is\(....\mu C\)
JEE Mains 2020 Medium - In the experimental setup of meter bridge shown in the figure, the null point is obtained at a distance of \(40\,cm\) from \(A\). If a \(10\,\Omega \) resistor is connected in series with \(R_1\), the null point shifts by \(10\,cm\). The resistance that should be connected in parallel with \(\left( {{R_1} + 10} \right)\,\Omega \) such that the null point shifts back to its initial position is .............. \(\Omega\)
JEE Mains 2019 Hard - The magnetic field in a region is given by \(\overrightarrow{ B }= B _{0}\left(\frac{ x }{ a }\right) \,\hat{ k }\). A square loop of side \(d\) is placed with its edges along the \(x\) and \(y\) axes. The loop is moved with a constant velocity \(\overrightarrow{ v }= v _{0} \hat{ i }\). The emf induced in the loop is:
JEE Mains 2021 Hard - A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field \(\vec{E}_1=E_0\hat{x}\). If another electric field \(\vec{E}_2=2E_0(\hat{y}+\hat{z})\) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?JEE Mains 2026 Hard
- A Carnot engine whose heat \(\operatorname{sinks}\) at \(27\,^{\circ} C\), has an efficiency of \(25 \%\). By how many degrees should the temperature of the source be changed to increase the efficiency by \(100 \%\) of the original efficiency \(?\)JEE Mains 2022 Hard
More PYQs from JEE Mains
- Let the area of the triangle with vertices \(A (1, \alpha)\), \(B (\alpha, 0)\) and \(C (0, \alpha)\) be \(4\, sq.\) units. If the point \((\alpha,-\alpha),(-\alpha, \alpha)\) and \(\left(\alpha^{2}, \beta\right)\) are collinear, then \(\beta\) is equal toJEE Mains 2022 Medium
- What is the dimensional formula of \(a b^{-1}\) in the equation? \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where letters have their usual meaning.JEE Mains 2024 Hard
- For \(k \in N\), let \(\frac{1}{\alpha(\alpha+1)(\alpha+2) \ldots(\alpha+20)}=\sum_{k=0}^{20} \frac{A_{k}}{a+k}\), where \(a\,>\,0\). Then the value of \(100\left(\frac{A_{14}+A_{15}}{A_{13}}\right)^{2}\) is equal to \(....\)JEE Mains 2021 Hard
- The perpendicular distance, of the line \(\frac{x-1}{2}=\frac{y+2}{-1}=\frac{z+3}{2}\) from the point \(\mathrm{P}(2,-10,1)\), is :JEE Mains 2025 Easy
- Given a thin convex lens (refractive index \(\mu_2\) ), kept in a liquid (refractive index \(\mu_1, \mu_1 \lt \mu_2\) ) having radii of curvatures \(\left|R_1\right|\) and \(\left|R_2\right|\). Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?JEE Mains 2025 Medium
- A tangent is drawn to the parabola \(y^{2}=6 x\) which is perpendicular to the line \(2 x + y =1\) Which of the following points does \(NOT\) lie on it ?JEE Mains 2021 Medium