JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
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
- A \(\frac{3}{7 \sqrt{2}} \frac{\mathrm{v}}{l}\)
- B \(\frac{3 \sqrt{2}}{7} \frac{v}{l}\)
- C \(\frac{4}{7} \frac{v}{l}\)
- D \(\frac{3}{7} \frac{v}{l}\)
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…
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 body of mass \(2\, kg\) moves under a force of \((2 \hat{ i }+3 \hat{ j }+5 \hat{ k }) \,N\). It starts from rest and was at the origin initially. After \(4 \,s\), its new coordinates are \((8, b, 20)\). The value of \(b\) is ........ . (Round off to the Nearest Integer)JEE Mains 2021 Medium
- The dimension of \(\sqrt{\frac{\mu_0}{\epsilon_0}}\) is equal to that of :
( \(\mu_0=\) Vacuum permeability and \(\epsilon_0=\) Vacuum permittivity)JEE Mains 2025 Medium - The current in a coil of self inductance \(2.0 \,H\) is increasing according to \(I =2 \sin \left( t ^{2}\right) A\). The amount of energy spent during the period when current changes from \(0\) to \(2\, A\) is......\(J.\)JEE Mains 2022 Medium
- Electric charge is transferred to an irregular metallic disk as shown in figure. If \(\sigma_1, \sigma_2, \sigma_3\) and \(\sigma_4\) are charge densities at given points then, choose the correct answer from the options given below:
JEE Mains 2025 Medium - A stream of a positively charged particles having \(\frac{ q }{ m }=2 \times 10^{11} \frac{ C }{ kg }\) and velocity \(\overrightarrow{ v }_0=3 \times 10^7 \hat{ i ~ m} / s\) is deflected by an electric field \(1.8 \hat{ j } kV / m\). The electric field exists in a region of \(10 cm\) along \(x\) direction. Due to the electric field, the deflection of the charge particles in the \(y\) direction is \(...........mm\)JEE Mains 2023 Medium
- A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.JEE Mains 2021 Medium
More PYQs from JEE Mains
- If a right circularcone having maximum volume, is inscribed in a sphere of radius \(3\, cm\), then the curved surface area (in \(cm^2\)) of this cone isJEE Mains 2018 Hard
- If \(1+\left(2+{ }^{49} C _{1}+{ }^{49} C _{2}+\ldots .+{ }^{49} C _{49}\right)\left({ }^{50} C _{2}+{ }^{50} C _{4}+\right.\) \(\ldots . .+{ }^{50} C _{ so }\) ) is equal to \(2^{ n } . m\), where \(m\) is odd, then \(n\) \(+m\) is equal to.JEE Mains 2022 Hard
- If \(z\) and \(\omega\) are two complex numbers such that \(|z \omega|=1\) and \(\arg (z)-\arg (\omega)=\frac{3 \pi}{2}\), then \(\arg \left(\frac{1-2 \bar{z} \omega}{1+3 \bar{z} \omega}\right)\) is: (Here arg(z) denotes the principal argument of complex number \(z\) )JEE Mains 2021 Hard
- Four fair dice are thrown independently \(27\) times. Then the expected number of times, at least two dice show up a three or a five, isJEE Mains 2020 Hard
- The series combination of two batteries, both of the same emf \(10 \mathrm{\;V},\) but different internal resistance of \(20\; \Omega\) and \(5\; \Omega,\) is connected to the parallel combination of two resistors \(30\; \Omega\) and \(\mathrm{R}\; \Omega .\) The voltage difference across the battery of internal resistance \(20\; \Omega\) is zero, the value of \(\mathrm{R}(\text { in } \Omega)\) isJEE Mains 2020 Hard
- The equation of the plane containing the line \(2x- 5y+ z = 3; x +y+ 4z = 5,\) and parallel to the plane, \(x + 3y+ 6z = 1,\) is:JEE Mains 2015 Medium