JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
Match List\(-I\) with List\(-II\)
| List \(-I\) | List \(-II\) |
| \((A)\) Moment of inertia of solid sphere of radius \((R)\) about any tangent | \((I)\) \(\frac{5}{3} MR ^{2}\) |
| \((B)\) Moment of inertia of hollow sphere of radius \((R)\) about any tangent | \((II)\) \(\frac{7}{5} MR ^{2}\) |
| \((C)\) Moment of inertia of circular ring of radius \((R)\) about its diameter. | \((III)\) \(\frac{1}{4} MR ^{2}\) |
| \((D)\) Moment of inertia of circular disc of radius \((R)\) about any diameter. | \((IV)\) \(\frac{1}{2} MR ^{2}\) |
- A \(A-II, B-II, C-IV, D-III\)
- B \(A-I, B-II, C-IV, D-III\)
- C \(A-II, B-I, C-III, D-IV\)
- D \(A-I, B-II, C-III, D-IV\)
Answer & Solution
Correct Answer
(A) \(A-II, B-II, C-IV, D-III\)
Step-by-step Solution
Detailed explanation
\(I _{0}= I _{ com }+ MR ^{2}\) (Parallel Axis theorem) \(I_{0}=\frac{2}{5} M^{2}+M^{2}\) \(I_{0}=\frac{7}{5} M R^{2}\) Hollow sphere \(I_{0}=I_{\text {com }}+M^{2}\) \(=\frac{2}{3} M^{2}+M^{2}=\frac{5}{3} M^{2}\) \(I _{1}+ I _{2}+ I _{3}\) (Perpendicular axis theorem) By…
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
- Two p-n junction diodes \(D _1\) and \(D _2\) are connected as shown in figure. A and B are input signals and C is the output. The given circuit will function as a ___________.
JEE Mains 2026 Hard - The threshold wavelength for photoelectric emission from a material is \(5500\,\mathring A\). Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a \(A.\) \(75\,W\) infra-red lamp \(B.\) \(10\,W\) infra-red lamp \(C.\) \(75\,W\) ultra-violet lamp \(D.\) \(10\,W\) ultra-violet lamp Choose the correct answer from the options given below :JEE Mains 2023 Medium
- An electric dipole has a fixed dipole moment \(\vec P\) which makes angle \(\theta \) with respect to \(x-\)axis. When subjected to an electric field \(\overrightarrow {{E_1}} \) \(=E\)\(\hat i\) it experiences a torque \(\overrightarrow {{T_1}} \) =\(\;\tau \hat k\) When subjected to another electric field \(\overrightarrow {{E_2}} = \sqrt 3 {E_1}\hat j\) it experiences torque \(\overrightarrow {{T_2}} \) = \( - \overrightarrow {{T_1}} \) The angle \(\theta \;\) is.......\(^o\)JEE Mains 2017 Hard
- A sample of radioactive material \(A\), that has an activity of \(10\, mCi\, (1\, Ci = 3.7 \times 10^{10}\, decays/s)\), has twice the number of nuclei as another sample of different radioactive material \(B\) which has an activity of \(20\, mCi\). The correct choices for half-lives of \(A\) and \(B\) would then be respectivelyJEE Mains 2019 Hard
- When a coil is connected across a \(20 \mathrm{~V}\) DC supply, it draws a current of \(5 \mathrm{~A}\). When it is connected across \(20 \mathrm{~V}, 50 \mathrm{~Hz}\) AC supply, it draws a current of \(4 \mathrm{~A}\). The self inductance of the coil is _______ \(\mathrm{mH}\). (Take \(\pi=3\) )JEE Mains 2024 Hard
- An electron in the ground state of the hydrogen atom has the orbital radius of \(5.3 \times 10^{-11} \mathrm{~m}\) while that for the electron in third excited state is \(8.48 \times 10^{-10} \mathrm{~m}\). The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is _______.JEE Mains 2025 Easy
More PYQs from JEE Mains
- A person has been using spectacles of power- \(1.0\) diopter for distant vision and a separate reading glass of power \(2.0\) diopters. What is the least distance of distinct vision for this person \(.......cm\)JEE Mains 2023 Hard
- The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly five 1 s and exactly three 2 s , is equal toJEE Mains 2025 Easy
- The set of all values of \(\lambda\) for which the equation \(\cos ^2 2 x-2 \sin ^4 x-2 \cos ^2 x=\lambda\)JEE Mains 2023 Hard
- A square is inscribed in the circle \(x^2+y^2-10 x-6 y+30=0\). One side of this square is parallel to \(y=x+3\). If \(\left(x_i, y_i\right)\) are the vertices of the square, then \(\sum\left(\mathrm{x}_{\mathrm{i}}^2+\mathrm{y}_{\mathrm{i}}^2\right)\) is equal to :JEE Mains 2024 Hard
- Let \(m_{1}, m_{2}\) be the slopes of two adjacent sides of a square of side a such that \(a^{2}+11 a+3\left(m_{2}^{2}+m_{2}^{2}\right)=220\). If one vertex of the square is \((10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))\), where \(\alpha \in\left(0, \frac{\pi}{2}\right)\) and the equation of one diagonal is \((\cos \alpha-\sin \alpha) x +(\sin \alpha+\cos \alpha) y =10\), then \(72 \left(\sin ^{4} \alpha+\cos ^{4} \alpha\right)+a^{2}-3 a+13\) is equal to.JEE Mains 2022 Hard
-

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance \(R_p=1 \Omega\) as shown in the figure. An external resistance of \(R_e=2 \Omega\) is connected via the sliding contact. The electric current in the circuit is :JEE Mains 2025 Medium