JEE Mains · Physics · STD 11 - Oscillations
- JEE Mains 2024
- Hard
- Numerical
An object of mass \(0.2 \mathrm{~kg}\) executes simple harmonic motion along \(\mathrm{x}\) axis with frequency of \(\left(\frac{25}{\pi}\right) \mathrm{Hz}\). At the position \(\mathrm{x}=0.04 \mathrm{~m}\) the object has kinetic energy \(0.5 \mathrm{~J}\) and potential energy \(0.4 \mathrm{~J}\) The amplitude of oscillation is _______ cm.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
\(\text { Total energy }=\text { K.E. }+ \text { P.E. }\)
\(\text { at } \mathrm{x}=0.04 \mathrm{~m}, \text { T.E. }=0.5+0.4=0.9 \mathrm{~J}\)
\(\text { T.E }=1 \mathrm{~m}^2 \mathrm{~A}^2=0.9\)
\(\quad=\frac{1}{2} \times 0.2\left(2 \pi \times \frac{25}{\pi}\right)^2 \times \mathrm{A}^2=0.9\)
\(\Rightarrow \mathrm{A}=0.06 \mathrm{~m}\)
\(\mathrm{~A}=6 \mathrm{~cm}\)
More questions from Physics
- The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is \(40\,cm.\) The area of the image is \(9\,times\) that of the square. The focal length of the lens is........\(cm\)JEE Mains 2013 Hard
- Two satellites \(A\) and \(B\) move round the earth in the same orbit. The mass of \(A\) is twice the mass of \(B\). The quantity which is same for the two satellites will be :JEE Mains 2023 Medium
- A plane electromagnetic wave of wavelength \(\lambda \) has an intensity \(I.\) It is propagating along the positive \(Y-\) direction. The allowed expressions for the electric and magnetic fields are given byJEE Mains 2018 Medium
- A thermometer graduated according to a linear scale reads a value \(x_0\) when in contact with boiling water, and \(x_0/3\) when in contact with ice. What is the temperature of an object in \({}^oC\), if this thermometer in the contact with the object reads \(x_0/2\) ?JEE Mains 2019 Hard
- In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across \(52\ cm\) of the potentiometer wire. If the cell is shunted by a resistance of \( 5\,\Omega\), a balance is found when the cell is connected across \(40\ cm\) of the wire. Find the internal resistance of the cell ........... \(\Omega\)JEE Mains 2018 Medium
- A proton and an \(\alpha\) -particle, having kinetic energies \(K _{ p }\) and \(K _{\alpha},\) respectively, enter into \(a\) magnetic field at right angles. The ratio of the radii of trajectory of proton to that of \(\alpha\) -particle is \(2: 1 .\) The ratio of \(K _{ p }: K _{\alpha}\) is :JEE Mains 2021 Medium
More PYQs from JEE Mains
- Match List\(-I\) with List\(-II\)
Choose the correct answer from the options given belowList\(-I\) List\(-II\) \((a)\) \(h\) (Planck's constant) \((i)\) \(\left[ M L T ^{-1}\right]\) \((b)\) \(E\) (kinetic energy) \((ii)\) \(\left[ M L ^{2} T ^{-1}\right]\) \((c)\) \(V\) (electric potential) \((iii)\) \(\left[ M L ^{2} T ^{-2}\right]\) \((d)\) \(P\) (linear momentum) \(( iv )\left[ M L ^{2} I ^{-1} T ^{-3}\right]\) JEE Mains 2021 Medium - A diverging lens with magnitude of focal length \(25\ cm\) is placed at a distance of \(15\ cm\) from a converging lens of magnitude of focal length \(20\ cm\). A beam of parallel light falls on the diverging lens. The final image formed isJEE Mains 2017 Medium