JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2022
- Hard
- Numerical
A rolling wheel of \(12 \,kg\) is on an inclined plane at position \(P\) and connected to a mass of \(3 \,kg\) through a string of fixed length and pulley as shown in figure. Consider \(PR\) as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom \(Q\) of the inclined plane \(P Q\) will be \(\frac{1}{2} \sqrt{ xgh } \,m / s\). The value of \(x\) is.............
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
Net loss in \(PE =\) Gain in \(KE\)
\(12 gh -3 gh =\frac{1}{2} 3 v ^{2}+\frac{1}{2} 12 v ^{2}+\frac{1}{2}\left[12 r ^{2}\right]\left(\frac{ v }{ r }\right)^{2}\)
\(9 gh =\frac{1}{2}[3+12+12] v ^{2}\)
\(v ^{2}=\frac{2 gh }{3} \Rightarrow v =\frac{1}{2} \sqrt{\frac{8}{3} gh }\)
\(x =\frac{8}{3} \simeq 3\)
More questions from Physics
- A metallic conductor of length \(1\; m\) rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity \(5 \;rad / s\). If the horizontal component of earth's magnetic field is \(0.2 \times 10^{-4} \;T\), then emf induced between the two ends of the conductor is .............JEE Mains 2022 Medium
- A person travelling on a straight line moves with a uniform velocity \(\mathrm{v}_1\) for a distance x and with a uniform velocity \(\mathrm{v}_2\) for the next \(\frac{3}{2} \mathrm{x}\) distance. The average velocity in this motion is \(\frac{50}{7} \mathrm{~m} / \mathrm{s}\). If \(\mathrm{v}_1\) is \(5 \mathrm{~m} / \mathrm{s}\) then \(\mathrm{v}_2=\) _________ \(\mathrm{m} / \mathrm{s}\).JEE Mains 2025 Easy
- The electric field of an electromagnetic wave in free space is represented as \(\vec{E}=E_0 \cos (\omega t-k z) \hat{i}\). The corresponding magnetic induction vector will be _______.JEE Mains 2024 Hard
- Two radioactive substances \(A\) and \(B\) have decay constants \(5\lambda \) and \(\lambda \) respectively. At \(t = 0\), a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become \((\frac {1}{e})^2\) will beJEE Mains 2019 Medium
- If two charges \(q _1\) and \(q _2\) are separated with distance ' \(d\) ' and placed in a medium of dielectric constant \(K\). What will be the equivalent distance between charges in air for the same electrostatic force?JEE Mains 2023 Medium
- Three concentric metal shells \(A, B\) and \(C\) of respective radii \(a, b\) and \(c (a < b < c)\) have surface charge densities \(+\sigma,-\sigma\) and \(+\sigma\) respectively. The potential of shell \(B\) isJEE Mains 2018 Hard
More PYQs from JEE Mains
- A \(15\,g\) mass of nitrogen gas is enclosed in a vessel at a temperature \(27\,^oC.\) Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about ...... \(kJ\) [Take \(R = 8.3\,J/K\,mole\) ]JEE Mains 2019 Medium
- \(2\, moles\) of helium gas is mixed with \(3\, moles\) of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume ....... \(J/mol\, K\) ? \((R = 8.3\, J/mol\, K)\)JEE Mains 2019 Hard
- The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass \(4\;kg\). (The coordinates of the same are shown in figure) are
JEE Mains 2020 Medium - A thin half ring of radius \(35\) cm is uniformly charged with a total charge of \(Q\) coulomb. If the magnitude of the electric field at centre of the half ring is \(100\) V/m, then the value of \(Q\) is _______ nC. (\(\epsilon_o = 8.85 \times 10^{-12}\) C\(^2\)/Nm\(^2\) and \(\pi = 3.14\))JEE Mains 2026 Medium
- Which of the following statement is not true about stopping potential \(\left(\mathrm{V}_0\right)\)?JEE Mains 2024 Hard
- The electrostatic potential due to an electric dipole at a distance '\(r\)' varies as _______.JEE Mains 2024 Hard