JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
A uniform sphere of mass \(500\; g\) rolls without slipping on a plane horizontal surface with its centre moving at a speed of \(5.00\; \mathrm{cm} / \mathrm{s}\). Its kinetic energy is
- A \(8.75 \times 10^{-4} \;\mathrm{J}\)
- B \(8.75 \times 10^{-3} \;\mathrm{J}\)
- C \(6.25 \times 10^{-4} \;\mathrm{J}\)
- D \(1.13 \times 10^{-} \;\mathrm{J}\)
Answer & Solution
Correct Answer
(A) \(8.75 \times 10^{-4} \;\mathrm{J}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{m}=0.5 \mathrm{kg}, \mathrm{v}=5 \mathrm{cm} / \mathrm{s}\) \(\mathrm{KE}\) in rolling \(=\frac{1}{2} \mathrm{mv}^{2}+\frac{1}{2} \mathrm{I} \omega^{2}\) \(=\frac{1}{2} \mathrm{mv}^{2}\left(1+\frac{\mathrm{K}^{2}}{\mathrm{R}^{2}}\right)\)…
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 \(1\) kg block subjected to two simultaneous forces \((2\hat{i} + 3\hat{j} + 4\hat{k})\) N and \((3\hat{i} - \hat{j} - 2\hat{k})\) N is moved a distance of \(25\) m along \((3\hat{i} - 4\hat{j})\) direction. The work done in this process is _____ J.JEE Mains 2026 Medium
- In a Young's double slit experiment, two slits are located 1.5 mm apart. The distance of screen from slits is 2 m and the wavelength of the source is 400 nm. If the 20 maxima of the double slit pattern are contained within the centre maximum of the single slit diffraction pattern, then the width of each slit is \(\mathrm{x} \times 10^{-3} \mathrm{~cm}\), where x -value is ________.JEE Mains 2025 Easy
- The equivalent resistance of the circuit shown below between points \(a\) and \(b\) is \(..........\Omega\)
JEE Mains 2023 Medium - The ratio of vapour densities of two gases at the same temperature is \(\frac{4}{25}\), then the ratio of r.m.s. velocities will be:JEE Mains 2025 Easy
- A cubical volume is bounded by the surfaces \(x =0, x = a , y =0, y = a , z =0, z = a\). The electric field in the region is given by \(\overrightarrow{ E }= E _0 \times \hat{ i }\). Where \(E _0=4 \times 10^4 NC ^{-1} m ^{-1}\). If \(a =2 cm\), the charge contained in the cubical volume is \(Q \times 10^{-14} C\). The value of \(Q\) is \(...........\) Take \(\left.\varepsilon_0=9 \times 10^{-12} C ^2 / Nm ^2\right)\)JEE Mains 2023 Medium
- The radiation corresponding to \(3 \rightarrow 2\) transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of \(5 \times 10^{-4} \,{T}\). Assume that the radius of the largest circular path followed by these electrons is \(7\, {mm}\), the work function of the metal is \(.....\,{eV}\) (Mass of electron \(=9.1 \times 10^{-31} \,{kg}\) )JEE Mains 2021 Hard
More PYQs from JEE Mains
- Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure \(90\) kPa and temperature \(400\) K. Keeping the temperature of one vessel constant at \(400\) K the second vessel temperature is raised to \(500\) K. The final pressure in the vessels is _______ kPa.JEE Mains 2026 Medium
- The number of distinct solutions of the equation \(\log _{\frac{1}{2}}|\sin x|=2-\log _{\frac{1}{2}}|\cos x|\) in the interval \([0,2 \pi],\) isJEE Mains 2020 Hard
- A solenoid having area \(A\) and length ' \(l\) ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :JEE Mains 2025 Easy
- Let \(C\) be a circle passing through the points \(A (2,-1)\) and \(B (3,4)\). The line segment \(AB\) is not a diameter of \(C\). If \(r\) is the radius of \(C\) and its centre lies on the circle \((x-5)^{2}+(y-1)^{2}=\frac{13}{2}\), then \(r^{2}\) is equal toJEE Mains 2022 Medium
- Let the area of the triangle with vertices \(A (1, \alpha)\), \(B (\alpha, 0)\) and \(C (0, \alpha)\) be \(4\, sq.\) units. If the point \((\alpha,-\alpha),(-\alpha, \alpha)\) and \(\left(\alpha^{2}, \beta\right)\) are collinear, then \(\beta\) is equal toJEE Mains 2022 Medium
- Let \(A(3, 0, -1), B(2, 10, 6)\) and \(C(1, 2, 1)\) be the vertices of a triangle and \(M\) be the midpoint of \(AC\). If \(G\) divides \(BM\) in the ratio, \(2 : 1\), then \(\cos \,\left( {\angle GOA} \right)\) (\(O\) being he origin) is equal toJEE Mains 2019 Hard