JEE Mains · Physics · STD 11 - 13. oscillations
The bob of a pendulum was released from a horizontal position. The length of the pendulum is \(10 \mathrm{~m}\). If it dissipates \(10 \%\) of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is : _______. [Use, \(\mathrm{g}: 10 \mathrm{~ms}^{-2}\) ]
- A \(6 \sqrt{5} \mathrm{~ms}^{-1}\)
- B \(5 \sqrt{6} \mathrm{~ms}^{-1}\)
- C \(5 \sqrt{5} \mathrm{~ms}^{-1}\)
- D \(2 \sqrt{5} \mathrm{~ms}^{-1}\)
Answer & Solution
Correct Answer
(A) \(6 \sqrt{5} \mathrm{~ms}^{-1}\)
Step-by-step Solution
Detailed explanation
\( \ell=10 \mathrm{~m} \) \( \text { Initial energy }=\mathrm{mg} \ell \) \( \text { So, } \frac{9}{10} \mathrm{mg} \ell=\frac{1}{2} \mathrm{mv}^2 \) \( \Rightarrow \frac{9}{10} \times 10 \times 10=\frac{1}{2} \mathrm{v}^2 \) \( \mathrm{v}^2=180 \)…
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 circular hole of radius \(\frac{R}{4}\) is made in a thin uniform disc having mass \(M\) and radius \(R\), as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point \(O\) and perpendicular to the plane of the disc is
JEE Mains 2017 Hard - Calculate the limit of resolution of a telescope objective having a diameter of \(200\, cm\), if it has to detect light of wavelength \(500\, nm\) coming from a starJEE Mains 2019 Easy
- Two identical thin biconvex lenses of focal length \(15\, cm\) and refractive index \(1.5\) are in contact with each other. The space between the lenses is filled with a liquid of refractive index \(1.25\). The focal length of the combination is \(cm\).
JEE Mains 2022 Hard - The total charge on the system of capacitance \(C _{1}=1\,\mu F , C _{2}=2\,\mu F , C _{3}=4\,\mu F\) and \(C _{4}=3\,\mu F\) connected in parallel is \(......\mu C\) (Assume a battery of \(20\,V\) is connected to the combination)JEE Mains 2022 Medium
- Which of the following circuits represents a forward biased diode?
Choose the correct answer from the options given below :JEE Mains 2025 Easy - To measure the temperature coefficient of resistivity \(\alpha\) of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of the semiconductor. The experiment is being conducted at \(25^{\circ} \mathrm{C}\) and resistance of the semiconductor arm is \(3 \mathrm{~m} \Omega\). Arm BC is cooled at a constant rate of \(2^{\circ} \mathrm{C} / \mathrm{s}\). If the galvanometer \(\mathrm{G}\) shows no deflection after \(10 \mathrm{~s}\), then \(\alpha\) is _______.
JEE Mains 2024 Hard
More PYQs from JEE Mains
- Inductance of a coil with \(10^4\) turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of \(10 \Omega\). The energy density in the inductor when the current reaches \(\left(\frac{1}{ e }\right)\) of its maximum value is \(\alpha \pi \times \frac{1}{ e ^2} J / m ^3\). The value of \(\alpha\) is __________ . \(\left(\mu_0=4 \pi \times 10^{-7} Tm / A \right)\).JEE Mains 2026 Easy
- The electric field in a region is given \(\overrightarrow{ E }=\left(\frac{3}{5} E _{0} \hat{ i }+\frac{4}{5} E _{0} \hat{ j }\right) \frac{ N }{ C } .\) The ratio of flux of reported field through the rectangular surface of area \(0.2\, m ^{2}\) (parallel to \(y - z\) plane) to that of the surface of area \(0.3\, m ^{2}\) (parallel to \(x - z\) plane \()\) is \(a : b ,\) where \(a =\) ............. [Here \(\hat{ i }, \hat{ j }\) and \(\hat{ k }\) are unit vectors along \(x , y\) and \(z-\)axes respectively]JEE Mains 2021 Hard
- A stone of mass \(900 \mathrm{~g}\) is tied to a string and moved in a vertical circle of radius \(1 \mathrm{~m}\) making \(10\ \mathrm{rpm}\). The tension in the string, when the stone is at the lowest point is _______. (if \(\pi^2=9.8\) and \(g=9.8 \mathrm{~m} / \mathrm{s}^2\) )JEE Mains 2024 Hard
- If \(n (2 n +1) \int_{0}^{1}\left(1- x ^{ n }\right)^{2 n } dx =1177 \int_{0}^{1}\left(1- x ^{ n }\right)^{2 n +1} dx\), then \(n \in N\) is equal to \(\dots\dots\)JEE Mains 2022 Hard
- Let the solution curve \(y=y(x)\) of the differential equation \(\left(4+x^{2}\right) d y-2 x\left(x^{2}+3 y+4\right) d x=0\) pass through the origin. Then \(y(2)\) is equal toJEE Mains 2022 Hard
- Let \(\frac{1}{{{x_1}}},\frac{1}{{{x_2}}},\frac{1}{{{x_3}}},.....,\) \(({x_i} \ne \,0\,for\,\,i\, = 1,2,....,n)\) be in \(A.P.\) such that \(x_1 = 4\) and \(x_{21} = 20.\) If \(n\) is the least positive integer for which \(x_n > 50,\) then \(\sum\limits_{i = 1}^n {\left( {\frac{1}{{{x_i}}}} \right)} \) is equal to.JEE Mains 2018 Hard