JEE Mains · Physics · STD 11 - 13. oscillations
In the given figure, a body of mass \(M\) is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant \(k,\) the frequency of oscillation of given body is :
- A \(\frac{1}{2 \pi} \sqrt{\frac{ k }{2 M }}\)
- B \(\frac{1}{2 \pi} \sqrt{\frac{2 k }{ Mg \sin \alpha}}\)
- C \(\frac{1}{2 \pi} \sqrt{\frac{2 k }{ M }}\)
- D \(\frac{1}{2 \pi} \sqrt{\frac{ k }{ Mg \sin \alpha}}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2 \pi} \sqrt{\frac{2 k }{ M }}\)
Step-by-step Solution
Detailed explanation
\(K _{ eq }= K _{1}+ K _{2}= K + K =2 K\) \(T =2 \pi \sqrt{\frac{ m }{ K _{ eq }}}=2 \pi \sqrt{\frac{ m }{2 K }}\) \(f =\frac{1}{ T }=\frac{1}{2 \pi} \sqrt{\frac{2 K }{ m }}\)
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 electric field at point p due to an electric dipole is E . The electric field at point R on equitorial line will be \(\frac{E}{x}\). The value of \(x\) is _______.
JEE Mains 2024 Medium - A porter lifts a heavy suitcase of mass \(80\, {kg}\) and at the destination lowers it down by a distance of \(80\, {cm}\) with a constant velocity. Calculate the workdone by the porter in lowering the suitcase. (take \(g=9.8\, {ms}^{-2}\) ) (In \({J}\))JEE Mains 2021 Medium
- A nucleus has mass number \(\alpha\) and radius \(R_{\alpha}\). Another nucleus has mass number \(\beta\) and radius \(R_{\beta}\). If \(\beta = 8\alpha\) then \(R_{\alpha}/R_{\beta}\) is :JEE Mains 2026 Medium
- The energy density associated with electric field \(\overrightarrow{ E }\) and magnetic field \(B\) of an electromagnetic wave in free space is given by ( \(\epsilon_0-\) permittivity of free space, \(\mu_0\) - permeability of free space)JEE Mains 2023 Medium
- Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion-(A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer.
Reason-(R) : The speed of light reduces in an optically denser medium than air while its frequency does not change.
In the light of the above statements, choose the most appropriate answer from the options given below :JEE Mains 2025 Easy - A rolling wheel of \(12 \,kg\) is on an inclined plane at position \(P\) and connected to a mass of \(3 \,kg\) through a string of fixed length and pulley as shown in figure. Consider \(PR\) as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom \(Q\) of the inclined plane \(P Q\) will be \(\frac{1}{2} \sqrt{ xgh } \,m / s\). The value of \(x\) is.............
JEE Mains 2022 Hard
More PYQs from JEE Mains
- A electron of hydrogen atom on an excited state is having energy \(E_n=-0.85 \mathrm{eV}\). The maximum number of allowed transitions to lower energy level is _______.JEE Mains 2024 Hard
- Monochromatic light is incident on a glass prism of angle \(A\). If the refractive index of the material of the prism is \(μ\), a ray, incident at an angle \(\theta\), on the face \(AB\) would get transmitted through the face \(AC\) of the prism provided
JEE Mains 2015 Hard - Let the circles \(C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2\) and \(C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2\) touch each other externally at the point \((6,6)\). If the point \((6,6)\) divides the line segment joining the centres of the circles \(C_1\) and \(C_2\) internally in the ratio \(2: 1\), then \((\alpha+\beta)+4\left(r_1^2+r_2^2\right)\) equalsJEE Mains 2024 Hard
- Let \(E_{1}: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, \mathrm{a}\,>\,\mathrm{b} .\) Let \(\mathrm{E}_{2}\) be another ellipse such that it touches the end points of major axis of \(E_{1}\) and the foci \(E_{2}\) are the end points of minor axis of \(E_{1}\). If \(E_{1}\) and \(E_{2}\) have same eccentricities, then its value is :JEE Mains 2021 Hard
- If the volume of a parallelopiped, whose coterminus edges are given by the vectors \(\overrightarrow{ a }=\hat{ i }+\hat{ j }+ n \hat{ k }, \quad \overrightarrow{ b }=2 \hat{ i }+4 \hat{ j }- n \hat{ k } \quad\) and \(\overrightarrow{ c }=\hat{ i }+ n \hat{ j }+3 \hat{ k } \quad( n \geq 0),\) is \(158 cu. Units\), thenJEE Mains 2020 Medium
- In \(SI\, units\), the dimensions of \(\sqrt {\frac{{{ \varepsilon _0}}}{{{\mu _0}}}} \) isJEE Mains 2019 Medium