JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
Two particles \(A, B\) are moving on two concentric circles of radii \(R_1\) and \(R_2\) with equal angular speed \(\omega \). At \(t = 0,\) their positions and direction of motion are shown in the figure The relative velocity \(\overrightarrow {{V_A}} - \overrightarrow {{V_B}} \) at \(t = \frac{\pi }{{2\omega }}\) is given by
- A \(\omega ({R_1} + {R_2})\,\hat i\)
- B \(-\omega ({R_1} + {R_2})\,\hat i\)
- C \(\omega ({R_2} - {R_1})\,\hat i\)
- D \(\omega ({R_1} - {R_2})\,\hat i\)
Answer & Solution
Correct Answer
(C) \(\omega ({R_2} - {R_1})\,\hat i\)
Step-by-step Solution
Detailed explanation
at \(t= 0\) \(at\,t = \frac{\pi }{{2\omega }}\) \({\overrightarrow V _A} = {\overrightarrow V _B} = - \omega {R_1}\hat i + \omega .{R_2}\hat i\) \( = \omega \left( {{R_2} - {R_1}} \right)\hat i\)
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 fringe width of \(\,6 mm\) was produced for two slits separated by \(1\, mm\) apart. The screen is placed \(10\, m\) away. The wavelength of light used is \('x'\, nm.\) The value of \('x'\) to the nearest integer isJEE Mains 2021 Medium
- A body of \(\mathrm{m} \mathrm{kg}\) slides from rest along the curve of vertical circle from point \(A\) to \(B\) in friction less path. The velocity of the body at \(B\) is _______. (given, \(\mathrm{R}=14 \mathrm{~m}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^2\) and \(\sqrt{2}=1.4\) )
JEE Mains 2024 Hard - A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength \(980\,\mathop A\limits^o \). The radius of the atom in the excited state, in terms of Bohr radius \(a_0,\) will be \((hc\,=\,12500\,eV-\mathop A\limits^o)\)JEE Mains 2019 Hard
- A parallel - plate capacitor with plate area \(A\) has separation \(d\) between the plates. Two dielectric slabs of dielectric constant \({K}_{1}\) and \({K}_{2}\) of same area \(\frac A2\) and thickness \(\frac d2\) are inserted in the space between the plates. The capacitance of the capacitor will be given by :
JEE Mains 2021 Hard - Two projectiles \(A\) and \(B\) are thrown with initial velocities of \(40\,m / s\) and \(60\,m / s\) at angles \(30^{\circ}\) and \(60^{\circ}\) with the horizontal respectively. The ratio of their ranges respectively is \(\left( g =10\,m / s ^2\right)\)JEE Mains 2023 Easy
- The number of air molecules per \(\mathrm{cm}^3\) increased from \(3 \times 10^{19}\) to \(12 \times 10^{19}\). The ratio of collision frequency of air molecules before and after the increase in number respectively is \(.........\)JEE Mains 2023 Medium
More PYQs from JEE Mains
- A thin \(1 \,m\) long rod has a radius of \(5\, mm\). A force of \(50\,\pi kN\) is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is \(0.01\, mm\), which of the following statements is false ?JEE Mains 2016 Easy
- Let [ ] denote the greatest integer function and \( f(x)=lim_{n\rightarrow\infty}\frac{1}{n^{3}}\sum_{k=1}^{n}[\frac{k^{2}}{3^{x}}] \) Then \( 12\sum_{j=1}^{x}f(j) \) is equal to ........... .JEE Mains 2026 Medium
- The de Broglie wavelength of an oxygen molecule at \(27^{\circ} C\) is \(x \times 10^{-12} m\). The value of \(x\) is (take Planck's constant \(=6.63 \times 10^{-34} J . s\), Boltzmann constant \(=1.38 \times 10^{-23} J / K\), mass of oxygen. Molecule \(\left.=5.31 \times 10^{-26} kg\right)\).JEE Mains 2026 Hard
- A man \(X\) has \(7\) friends, \(4\) of them are ladies and \(3\) are men. His wife \(Y\) also has \(7\) friends, \(3\) of them are ladies and \(4\) are men. Assume \(X\) and \(Y\) have no comman friends. Then the total number of ways in which \(X\) and \(Y\) together can throw a party inviting \(3\) ladies and \(3\) men, so that \(3\) friends of each of \(X\) and \(Y\) are in this party is :JEE Mains 2017 Hard
- Let a function \(f: R \rightarrow R\) be defined as \(f(x)=\sin x-e^{x} \,\,\,\, \text { if } x \leq 0\) \(\quad\quad\quad a+[-x] \,\,\,\, \text { if } 0\,<\,x\,<\,1\) \(\quad\quad\quad 2 x-b \,\,\,\,\,\,\,\, \text { if } \geq 1\) where \([\mathrm{x}]\) is the greatest integer less than or equal to \(\mathrm{x}\). If \(\mathrm{f}\) is continuous on \(\mathrm{R}\), then \((\mathrm{a}+\mathrm{b})\) is equal to:JEE Mains 2021 Hard
- If the matrix \(A=\left(\begin{array}{cc}0 & 2 \\ K & -1\end{array}\right)\) satisfies \(A\left(A^{3}+3 I\right)=2 I\) then the value of \(\mathrm{K}\) is :JEE Mains 2021 Hard