JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2020
- Hard
- MCQ
Consider a uniform rod of mass \(\mathrm{M}=4 \mathrm{m}\) and length \(\ell\) pivoted about its centre. A mass \(m\) moving with velocity \(v\) making angle \(\theta=\frac{\pi}{4}\) to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(\frac{3 \sqrt{2}}{7} \frac{v}{l}\)
Step-by-step Solution
Detailed explanation
Let angular velocity of the system after collision be \(\omega\).
By conservation of angular momentum about the hinge
\(\mathrm{m}\left(\frac{\mathrm{v}}{\sqrt{2}}\right)\left(\frac{\ell}{2}\right)=\left[\frac{4 \mathrm{m} \ell^{2}}{12}+\frac{\mathrm{m} \ell^{2}}{4}\right] \omega\)
On solving
\(\omega=\frac{3 \sqrt{2}}{7}\left(\frac{v}{l}\right)\)
More questions from Physics
- In a meter bridge experiment the balance point in obtained if the gaps are closed by \(2\,\Omega\) and \(3\,\Omega\). A shunt of \(x\,\Omega\) is added to \(3\,\Omega\) resistor to shift the balancing point by \(22.5\,cm\). The value of \(X\) is \(................\)JEE Mains 2023 Medium
- A uniform rod \(A B\) of mass \(2 \mathrm{~kg}\) and Length \(30 \mathrm{~cm}\) at rest on a smooth horizontal surface. An impulse of force \(0.2\ \mathrm{Ns}\) is applied to end \(B.\) The time taken by the rod to turn through at right angles will be \(\frac{\pi}{\mathrm{x}}\ \mathrm{s}\), where X = _______.JEE Mains 2024 Hard
- One main scale division of a vernier caliper is equal to \(m\) units. If \(n^{\text {th }}\) division of main scale coincides with \((n+1)^{\mathrm{th}}\) division of vernier scale, the least count of the vernier caliper is _______.JEE Mains 2024 Hard
- A satellite is revolving in a circular orbit at a height \(h\) from the earth surface, such that \(h < < R\) where \(R\) is the radius of the earth. Assuming that the effect of earth’s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth isJEE Mains 2019 Medium
- On celcius scale the temperature of body increases by \(40^{\circ} \mathrm{C}\). The increase in temperature on Fahrenheit scale is _______.JEE Mains 2024 Hard
- A Zener of breakdown voltage \(V_{z}=8\,V\) and maximum zener current, \(I _{ ZM }=10\,mA\) is subjected to an input voltage \(V _{ i }=10\,V\) with series resistance \(R=100\,\Omega\). In the given circuit \(R_{L}\) represents the variable load resistance. The ratio of maximum and minimum value of \(R_{L}\) is
JEE Mains 2022 Hard
More PYQs from JEE Mains
- The dimensions of angular momentum , latent heat and capacitance are, respectively.JEE Mains 2013 Hard
- Moment of inertia of a cylinder of mass \(M,\) length \(L\) and radius \(R\) about an axis passing through its centre and perpendicular to the axis of the cylinder is \(I = M \left(\frac{ R ^{2}}{4}+\frac{ L ^{2}}{12}\right) .\) If such a cylinder is to be made for a given mass of material, the ratio \(\frac LR\) for it to have minimum possible \(I\) isJEE Mains 2020 Hard
- An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and \(2 \sqrt{3}\) (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is _________ .JEE Mains 2026 Easy
- A single slit of width \(0.1\, mm\) is illuminated by a parallel beam of light of wavelength \(6000\,\mathop A\limits^o \) and diffraction bands are observed on a screen \(0.5\, m\) from the slit. The distance of the third dark band from the central bright band is........\(mm\)JEE Mains 2017 Medium