JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A solid cylinder and a solid sphere, having same mass \(M\) and radius \(R\), roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be.
- A \(\sqrt{\frac{5}{3}}\)
- B \(\sqrt{\frac{4}{5}}\)
- C \(\sqrt{\frac{3}{5}}\)
- D \(\sqrt{\frac{14}{15}}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{\frac{14}{15}}\)
Step-by-step Solution
Detailed explanation
\(V=\sqrt{\frac{2 g H}{1+ k ^{2} / R ^{2}}}\) \(\frac{V_{\text {cylinder }}}{V_{\text {sphere }}}=\sqrt{\frac{\left(1+ k ^{2} / R ^{2}\right)_{\text {sphere }}}{\left(1+ k ^{2} / R ^{2}\right)_{\text {cylinder }}}}\)…
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
- \(2\, kg\) of a monoatomic gas is at a pressure of \(4\times10^4\, N/m^2\). The density of the gas is \(8\, kg/m^3\). What is the order of energy of the gas due to its thermal motion ?JEE Mains 2019 Medium
- Two wires \(A\) and \(B\) are made up of the same material and have the same mass. Wire A has radius of \(2.0 \mathrm{~mm}\) and wire \(B\) has radius of \(4.0 \mathrm{~mm}\). The resistance of wire B is \(2 \Omega\). The resistance of wire \(\mathrm{A}\) is _______ \(\Omega\).JEE Mains 2024 Hard
- Light wave traveling in air along \(x\)-direction is given by \(E _{ y }=540 \sin \pi \times 10^{4}( x - ct ) Vm ^{-1}\). Then, the peak value of magnetic field of wave will be \(\dots \times 10^{-7}\,T\) (Given \(c =3 \times 10^{8}\,ms ^{-1}\) )JEE Mains 2022 Easy
- A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of \(f_1\) in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of \(\mathrm{f}_2\) when it is immersed in a liquid of refractive index 1.2 . If both the lenses are made of same glass of refractive index 1.5 , the ratio of \(f_1\) and \(f_2\) will be _______.JEE Mains 2025 Hard
- In the electric network shown, when no current flows through the \(4\, \Omega \) resistor in the arm \(EB\), the potential difference between the points \(A\) and \(D\) will be ............... \(V\)
JEE Mains 2015 Hard - A system consists of two types of gas molecules \(A\) and \(B\) having same number density \(2 \times\) \(10^{25}\, / {m}^{3}\). The diameter of \({A}\) and \({B}\) are \(10\, \stackrel{\circ}{{A}}\) and \(5\, \stackrel{\circ}{{A}}\) respectively. They suffer collision at room temperature. The ratio of average distance covererd by the molecule \(A\) to that of \(B\) between two successive collision is \(.....\,\times 10^{-2}\)JEE Mains 2021 Medium
More PYQs from JEE Mains
- A plane passing through the points \((0, -1, 0)\) and \((0, 0, 1)\) and making an angle \(\frac {\pi }{4}\) with plane \(y -z + 5 = 0,\) also passes through the pointJEE Mains 2019 Hard
- Consider the function \(\mathrm{f}:(0,2) \rightarrow \mathrm{R}\) defined by \(f(x)=\frac{x}{2}+\frac{2}{x}\) and the function\( g(x)\) defined by \(g(x)=\left\{\begin{array}{cc}\min \{f(t)\}, & 0 < t \leq x \text { and } 0 < x \leq 1 \\ \frac{3}{2}+x, & 1 < x< 2\end{array}\right.\). ThenJEE Mains 2024 Hard
- A light rope is wound around a hollow cylinder of mass \(5\,kg\) and radius \(70\,cm\). The rope is pulled with a force of \(52.5\,N\). The angular acceleration of the cylinder will be.....\( {rad \,s}{ }^{-2}\).JEE Mains 2023 Medium
- When a coil is placed in a time dependent magnetic field the power dissipated in it is \(P\). The number of turns, area of the coil and radius of the coil wire are \(N\), \(A\) and \(r\) respectively. For a second coils number of turns, area of the coil and radius of the coil wire are \(2N\), \(2A\) and \(3r\) respectively. When the first coil is replaced with second coil the power dissipated in it is \(\sqrt{2}\,\alpha P\). The value of \(\alpha\) is _______.JEE Mains 2026 Hard
- 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 beJEE Mains 2025 Medium
- The given circuit works as :
JEE Mains 2026 Easy