JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
One end of a straight uniform \(1\; \mathrm{m}\) long bar is pivoted on horizontal table. It is released from rest when it makes an angle \(30^{\circ}\) from the horizontal (see figure). Its angular speed when it hits the table is given as \(\sqrt{\mathrm{n}}\; \mathrm{s}^{-1},\) where \(\mathrm{n}\) is an integer. The value of \(n\) is
- A \(10\)
- B \(13\)
- C \(15\)
- D \(18\)
Answer & Solution
Correct Answer
(C) \(15\)
Step-by-step Solution
Detailed explanation
From mechanical energy conservation, \(\mathrm{U}_{\mathrm{i}}+\mathrm{K}_{\mathrm{i}}=\mathrm{U}_{\mathrm{f}}+\mathrm{K}_{\mathrm{r}}\) \(\Rightarrow \mathrm{mg} \frac{\ell}{2} \sin 30^{\circ}+0=0+\frac{1}{2} \mathrm{I} \omega^{2}\)…
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
- The magnitude of vectors \(\overrightarrow{ OA }, \overrightarrow{ OB }\) and \(\overrightarrow{ OC }\) in the given figure are equal. The direction of \(\overrightarrow{ OA }+\overrightarrow{ OB }-\overrightarrow{ OC }\) with \(x\)-axis will be
JEE Mains 2021 Hard - A ring of mass \(M\) and radius \(R\) is rotating about its axis with angular velocity \(\omega \). Two identical bodies each of mass \(m\) are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will beJEE Mains 2013 Hard
- A heavy ball of mass \(M\) is suspended from the ceiling of car by a light string of mass \(m (m << M)\). When the car is at rest, the speed of transverse waves in the string is \(60\, ms^{-1}\). When the car has acceleration \(a\) , the wave-speed increases to \(60.5\, ms^{-1}\). The value of \(a\) , in terms of gravitational acceleration \(g\) is closest toJEE Mains 2019 Hard
- A fringe width of \(\,6 mm\) was produced for two slits separated by \(1\, mm\) apart. The screen is placed \(10\, m\) away. The wavelength of light used is \('x'\, nm.\) The value of \('x'\) to the nearest integer isJEE Mains 2021 Medium
- Three charges \(+Q, q, +Q\) are placed respectively, at distance, \(0, \frac d2\) and \(d\) from the origin, on the \(x-\) axis. If the net force experienced by \(+Q\), placed at \(x = 0\), is zero, then value of \(q\) isJEE Mains 2019 Hard
- At a given point of time the value of displacement of a simple harmonic oscillator is given as \(y = A \cos \left(30^{\circ}\right)\). If amplitude is \(40\,cm\) and kinetic energy at that time is \(200\, J\), the value of force constant is \(1.0 \times 10^{ x }\,Nm ^{-1}\). The value of \(x\) is ......JEE Mains 2023 Hard
More PYQs from JEE Mains
- The coefficient of static friction between a wooden block of mass \(0.5\, kg\) and a vertical rough wall is \(0.2\) The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be \(N\) \(\left[ g =10\, ms ^{-2}\right]\)JEE Mains 2021 Medium
- If the maximum value of the term independent of \(t\) in the expansion of \(\left( t ^{2} x ^{\frac{1}{5}}+\frac{(1- x )^{\frac{1}{10}}}{ t }\right)^{15}, x \geq 0\), is \(K\), then \(8\,K\) is equal to \(....\)JEE Mains 2022 Hard
- \(1\) mole of rigid diatomic gas performs a work of \(Q / 5\) when heat \(Q\) is supplied to it. The molar heat capacity of the gas during this transformation is \(\frac{ x R }{8},\) The value of \(x\) is \(\ldots \ldots \ldots .\) \([ K =\) universal gas constant \(]\)JEE Mains 2021 Hard
- Locus of the image of point \( (2,3)\) in the line \(\left( {2x - 3y + 4} \right) + k\left( {x - 2y + 3} \right) = 0,k \in R\) is a:JEE Mains 2015 Hard
- The percentage decrease in the weight of a rocket, when taken to a height of \(32 km\) above the surface of earth will, be\(.....\%\) (Radius of earth \(=6400\,km\) )JEE Mains 2022 Medium
- Let \(A\) be a \(3 \times 3\) real matrix such that \(\mathrm{A}\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)=2\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right), \mathrm{A}\left(\begin{array}{l}-1 \\ 0 \\ 1\end{array}\right)=4\left(\begin{array}{l}-1 \\ 0 \\ 1\end{array}\right), \mathrm{A}\left(\begin{array}{l}0 \\ 1 \\ 0\end{array}\right)=2\left(\begin{array}{l}0 \\ 1 \\ 0\end{array}\right)\). Then, the system \((A-3 I)\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)\) hasJEE Mains 2024 Hard