JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A string is wound around a hollow cylinder of mass \(5\, kg\) and radius \(0.5\,m\). If the string is now pulled with a horizontal force of \(40\, N\), and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be ......... \(rad/s^2\) .(Neglect the mass and thickness of the string)
- A \(20\)
- B \(16\)
- C \(12\)
- D \(10\)
Answer & Solution
Correct Answer
(B) \(16\)
Step-by-step Solution
Detailed explanation
\(40 + f = m\left( {R\alpha } \right)\,\,\,\,\,\,\,\,...\left( i \right)\) \(40 \times R - f \times R = mR = {2^\alpha }\) \(40 - f = mR\alpha \,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)\) From \((i)\) and \((ii)\) \(\alpha = \frac{{40}}{{mR}} = 16\)
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 capacitor of capacitance \(\mathrm{C}\) and potential \(\mathrm{V}\) has energy \(E\). It is connected to another capacitor of capacitance \(2 \mathrm{C}\) and potential \(2 \mathrm{~V}\). Then the loss of energy is \(\frac{x}{3} E\), where \(\mathrm{x}\) is _______.JEE Mains 2024 Hard
- \(10\) divisions on the main scale of a Vernier calliper coincide with \(11\) divisions on the Vernier scale. If each division on the main scale is of \(5\) units, the least count of the instrument is _______.JEE Mains 2024 Hard
- A tuning fork resonates with a sonometer wire of length \(1 \mathrm{~m}\) stretched with a tension of \(6 \mathrm{~N}\). When the tension in the wire is changed to \(54 \mathrm{~N}\), the same tuning fork produces \(12\) beats per second with it. The frequency of the tuning fork is _______ \(\mathrm{Hz}\).JEE Mains 2024 Medium
- A hydrogen atom in ground state is given an energy of \(10.2 \mathrm{eV}\). How many spectral lines will be emitted due to transition of electrons?JEE Mains 2024 Medium
- Consider two satellites \(S_{1}\) and \(S_{2}\) with periods of revolution \(1\, hr\). and \(8\, hr\). respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite \(S_{1}\) to the angular velocity of satellites \(S _{2}\) isJEE Mains 2021 Medium
- The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength \(6630 \; \mathring A\) is \(0.42 \; V\). If the threshold frequency is \(x \times\) \(10^{13} / s\), where \(x\) is\(\dots\) (nearest integer). (Given, speed light \(=3 \times 10^{8} \; m / s\), Planck's constant \(=6.63 \times 10^{-34} \; Js\) )JEE Mains 2022 Medium
More PYQs from JEE Mains
- Two conductors have the same resistances at \(0^{\circ} \mathrm{C}\) but their temperature coefficients of resistance are \(\alpha_1\) and \(\alpha_2\). The respective temperature coefficients for their series and parallel combinations are _______.JEE Mains 2024 Hard
- Let \(\quad f:(-\infty, \infty)-\{0\} \rightarrow R\) be a differentiable function such that \(f^{\prime}(1)=\lim _{a \rightarrow \infty} a^2 f\left(\frac{1}{a}\right)\). Then \(\lim _{a \rightarrow \infty} \frac{a(a+1)}{2} \tan ^{-1}\left(\frac{1}{a}\right)+a^2-2 \log _e a\) is equal toJEE Mains 2024 Hard
- Let \(y=y(x)\) be the solution curve of the differential equation
\(x\left(x^2+e^x\right) d y+\left(e^x(x-2) y-x^3\right) d x=0, x \gt 0\) passing through the point \((1,0)\). Then \(y(2)\) is equal to :JEE Mains 2025 Medium - If P is a point on the circle \( x^{2}+y^{2}=4 \), Q is a point on the straight line \( 5x+y+2=0 \) and \( x-y+1=0 \) is the perpendicular bisector of PQ, then 13 times the sum of abscissa of all such point P is ........... .JEE Mains 2026 Hard
- A machine gun of mass \(10\,kg\) fires \(20\,g\) bullets at the rate of \(180\) bullets per minute with a speed of \(100\,m s ^{-1}\) each. The recoil velocity of the gun is \(.............\,m/s\)JEE Mains 2023 Easy
- Lines are drawn parallel to the line \(4x -3y + 2 = 0\) at a distance \(\frac {3}{5}\) from the origin. Then which one of the following points lies on any of these lines?JEE Mains 2019 Hard