JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A uniform cylinder of mass \(M\) and radius \(R\) is to be pulled over a step of height \(a (a < R\)) by applying a force \(F\) at its centre \('O'\) perpendicular to the plane through the axes of the cylinder on the edge of the step ( see figure). The minimum value of \(F\) required is
- A \(Mg \sqrt{1-\frac{ a ^{2}}{ R ^{2}}}\)
- B \(Mg \sqrt{\left(\frac{ R }{ R - a }\right)^{2}-1}\)
- C \(Mg \frac{ a }{ R }\)
- D \(M g \sqrt{1-\left(\frac{R-a}{R}\right)^{2}}\)
Answer & Solution
Correct Answer
(D) \(M g \sqrt{1-\left(\frac{R-a}{R}\right)^{2}}\)
Step-by-step Solution
Detailed explanation
To Step up, \(F \times R \geq M g \times X\) \(\Rightarrow F_{\min }=\frac{M g}{R} \times \sqrt{R^{2}-(R-a)^{2}}\) \(\quad\quad\quad\,=M g \sqrt{1-\left(\frac{R-a}{R}\right)^{2}}\)
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
- The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is
JEE Mains 2023 Medium - Consider two containers \(A\) and \(B\) containing monoatomic gases at the same Pressure \((P)\), Volume \((V)\) and Temperature \((T)\). The gas in \(A\) is compressed isothermally to \(\frac{1}{8}\) of its original volume while the gas \(B\) is compressed adiabatically to \(\frac{1}{8}\) of its original volume. The ratio of final pressure of gas in \(B\) to that of gas in \(A\) is ...........JEE Mains 2023 Medium
- A mass \('m'\) is supported by a massless string wound around a uniform hollow cylinder of mass \(m\) and radius \(R\). If the string does not slip on the cylinder, with what acceleration will the mass fall on release?
JEE Mains 2014 Medium - If speed \((V)\), acceleration \((A)\) and force \((F)\) are considered as fundamental units, the dimension of Young’s modulus will beJEE Mains 2023 Hard
- An electron is travelling with a velocity \(v\) in free space and when it enters a medium, its velocity is reduced by \(20\%\). The de Broglie wavelength of electron in the medium is \(\alpha\lambda_0\), where \(\lambda_0\) is its de Broglie wavelength in free space. The value of \(\alpha\) is _______.JEE Mains 2026 Medium
- For a transistor to act as a switch, it must be operated inJEE Mains 2022 Medium
More PYQs from JEE Mains
- From a solid sphere of mass \(M\) and radius \(R\), a spherical portion of radius \(R/2\) is removed, as shown in the figure. Taking gravitational potential \(V = 0\) at \(r = \infty\), the potential at the centre of the cavity thus formed is
( \(G =\) gravitational constant)
JEE Mains 2015 Hard - The value of \(\int_{-2}^{2}\left|3 x^{2}-3 x-6\right| d x\) is ...... .JEE Mains 2021 Hard
- Let \(\theta\) be the angle between the vectors \(\vec{a}\) and \(\vec{b}\), where \(|\vec{a}|=4,|\vec{b}|=3 \quad \theta \in\left(\frac{\pi}{4}, \frac{\pi}{3}\right)\). Then \(|(\vec{a}-\vec{b}) \times(\vec{a}+\vec{b})|^{2}+4(\vec{a} \cdot \vec{b})^{2}\) is equal toJEE Mains 2022 Medium
- Given a sequence of \(4\) numbers, first three of which are in \(G.P.\) and the last three are in \(A.P\). with common difference six. If first and last terms in this sequence are equal, then the last term isJEE Mains 2013 Hard
- If the mean and the standard deviation of the data \(3,5,7, a, b\) are \(5\) and \(2\) respectively, then \(a\) and \(b\) are the roots of the equationJEE Mains 2020 Hard
- Let the shortest distance between the lines \(\frac{x-3}{3}=\frac{y-\alpha}{-1}=\frac{z-3}{1}\) and \(\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-\beta}{4}\) be \(3 \sqrt{30}\). Then the positive value of \(5 \alpha+\beta\) isJEE Mains 2025 Easy