JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2019
- Hard
- MCQ
Two masses \(m\) and \(\frac{m}{2}\) are connected at the two ends of a massless rigid rod of length \(l\). The rod is suspended by a thin wire of torsional constant \(k\) at the centre of mass of the rodmass system (see figure). Because of torsional constant \(k\), the restoring torque is \(\tau = k\,\theta \) for angular displacement \(\theta \). If the rod is rotated by \(\theta _0\) and released, the tension in it when it passes through its mean position will be
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(\frac{{k\,\theta _0^2}}{l}\)
Step-by-step Solution
Detailed explanation
\(\omega \)\( = \sqrt {\frac{K}{I}} \,\,\,;\,\,\,\omega = {\theta _0} \times \Omega \)
\(T = m{\omega ^2}\frac{\ell }{3}\)
\(T = m{\omega ^2}\frac{\ell }{3}{\theta _0}\frac{k}{I}\) where \(\,l = m\frac{{{\ell ^2}}}{3}\)
\(\,\,\,\,\, = \frac{{\theta _0^2k}}{\ell }\)
More questions from Physics
- The velocity at which \(6\) kg mass (shown in figure) strikes the ground when it is released from a height of \(6\) m above the ground is __________ m/s. Assume pulley is massless and string is light and inextensible. (Take g \(= 10\) m/s\(^2\))
JEE Mains 2026 Medium - Match List - I with List - II.
List - I List - II (A) Magnetic induction (I) Ampere meter2 (B) Magnetic intensity (II) Weber (C) Magnetic flux (III) Gauss (D) Magnetic moment (IV) Ampere meter
Choose the correct answer from the options given below :JEE Mains 2025 Medium - An object of mass ' m ' is projected from origin in a vertical \(x y\) plane at an angle \(45^{\circ}\) with the x axis with an initial velocity \(\mathrm{v}_0\). The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity]JEE Mains 2025 Easy
- Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.
Reason (R) : For a central force field the angular momentum is a constant.
In the light of the above statements, choose the most appropriate answer from the options given below :JEE Mains 2025 Easy - A spherically symmetric charge distribution is characterised by a charge density having the following variations \(\rho (r)\, = \,{\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(r < R\) \(\rho (r)\,=\,0\) for \(r\, \ge \,R\) Where \(r\) is the distance from the centre of the charge distribution \(\rho _0\) is a constant. The electric field at an internal point \((r < R)\) isJEE Mains 2014 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
More PYQs from JEE Mains
- The volume \(V\) of an enclosure contains a mixture of three gases, \(16\, g\) of oxygen, \(28\, g\) of nitrogen and \(44\, g\) of carbon dioxide at absolute temperature \(T\). Consider \(R\) as universal gas constant. The pressure of the mixture of gases isJEE Mains 2021 Medium
- A person travels \(x\) distance with velocity \(v_1\) and then \(x\) distance with velocity \(v_2\) in the same direction. The average velocity of the person is \(v\), then the relation between \(v , v _1\) and \(v _2\) will be :JEE Mains 2023 Medium
- Three vectors \(\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}\) and \(\overrightarrow{\mathrm{OR}}\) each of magnitude \(A\) are acting as shown in figure. The resultant of the three vectors is \(A \sqrt{x}\). The value of \(x\) is _______.
JEE Mains 2024 Hard