JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A uniform solid cylinder of mass ' \(m\) ' and radius ' \(r\) ' rolls along an inclined rough plane of inclination \(45^{\circ}\). If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be
- A \(\frac{1}{\sqrt{2}} \mathrm{~g}\)
- B \(\frac{1}{3 \sqrt{2}} \mathrm{~g}\)
- C \(\frac{\sqrt{2} \mathrm{~g}}{3}\)
- D \(\sqrt{2} g\)
Answer & Solution
Correct Answer
(C) \(\frac{\sqrt{2} \mathrm{~g}}{3}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & a=\frac{\mathrm{g} \sin \theta}{1+\frac{\mathrm{I}}{\mathrm{mR}^2}} \\ & a=\frac{\frac{g}{\sqrt{2}}}{1+\frac{1}{2}}=\frac{2 \frac{g}{\sqrt{2}}}{3}=\frac{\sqrt{2} g}{3}\end{aligned}\)
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 deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If \(r_{d}\) and \(r_{p}\) are the radii of their circular paths respectively, then the ratio \(\frac{r_{d}}{r_{p}}\) will be \(\sqrt{ x }: 1\) where \(x\) is ..........JEE Mains 2022 Medium
- In the figure shown, after the switch \(‘S’\) is turned from position \(‘A’\) to position \(‘B’\), the energy dissipated in the circuit in terms of capacitance \(‘C’\) and total charge \(‘Q’\) is
JEE Mains 2019 Hard - Find out the surface charge density at the intersection of point \(x =3\, m\) plane and \(x\) -axis, in the region of uniform line charge of \(8\, nC / m\) lying along the \(z\) -axis in free space.JEE Mains 2021 Hard
- The value of current \(i_{1}\) flowing from \(A\) to \(C\) in the circuit diagram is\(.......A\)
JEE Mains 2020 Medium - Let the moment of inertia of a hollow cylinder of length \(30\, cm\) (inner radius \(10\, cm\) and outer radius \(20\, cm\)), about its axis be \(I\). The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also \(I\), is ......... \(cm\).JEE Mains 2019 Hard
- A ball is thrown vertically upward with an initial velocity of \(150\,m / s\). The ratio of velocity after \(3\,s\) and \(5\,s\) is \(\frac{x+1}{x}\). The value of \(x\) is \(...........\) Take \(\left(g=10\,m / s ^2\right)\)JEE Mains 2023 Medium
More PYQs from JEE Mains
- Suppose the line \(\frac{x-2}{\alpha}=\frac{y-2}{-5}=\frac{z+2}{2}\) lies on the plane \(x+3 y-2 z+\beta=0 .\) Then \((\alpha+\beta)\) is equal to ... .JEE Mains 2021 Easy
- The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by
JEE Mains 2019 Medium - The number of real roots of the equation \(\mathrm{x}|\mathrm{x}-2|+3|\mathrm{x}-3|+1=0\) is :JEE Mains 2025 Medium
- An angle between the lines whose direction cosines are given by the equations, \(l+ 3m + 5n\, = 0\) and \(5lm -2mn + 6nl = 0\) , isJEE Mains 2018 Hard
- Let three vectors \(\overrightarrow{\mathrm{a}}=\alpha \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}\), \(\vec{b}=5 \hat{i}+3 \hat{j}+4 \hat{k}, \vec{c}=x \hat{i}+y \hat{j}+z \hat{k}\) from a triangle such that \(\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}\) and the area of the triangle is \(5 \sqrt{6}\). if \(\alpha\) is a positive real number, then \(|\overrightarrow{\mathrm{c}}|^2\) is :JEE Mains 2024 Hard
- A ratio of the \(5^{th}\) term from the beginning to the \(5^{th}\) term from the end in the binomial expansion of \(\left( {{2^{1/3}} + \frac{1}{{2{{\left( 3 \right)}^{1/3}}}}} \right)^{10}\) isJEE Mains 2019 Hard