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 :

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{2 \pi} \sqrt{\frac{2 k }{ M }}\)

Step-by-step Solution

Detailed explanation

\(K _{ eq }= K _{1}+ K _{2}= K + K =2 K\)

\(T =2 \pi \sqrt{\frac{ m }{ K _{ eq }}}=2 \pi \sqrt{\frac{ m }{2 K }}\)

\(f =\frac{1}{ T }=\frac{1}{2 \pi} \sqrt{\frac{2 K }{ m }}\)

Same subject

Magnetic materials used for making permanent magnets \((P)\) and magnets in a transformer \((T)\) have different properties of the following, which property best matches for the type of magnet required \(?\)

JEE Mains 2020 Medium
In a series \(L R\) circuit \(X_{L}=R\) and power factor of the circuit is \(P _{1}\). When capacitor with capacitance \(C\) such that \(X _{ L }= X _{ C }\) is put in series, the power factor becomes \(P_{2}\). The ratio \(\frac{ P _{1}}{ P _{2}}\) is

JEE Mains 2022 Medium
A spherically symmetric charge distribution is characterised by a charge density having the following variations \(\rho (r)\, = \,{\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(r < R\) \(\rho (r)\,=\,0\) for \(r\, \ge \,R\) Where \(r\) is the distance from the centre of the charge distribution \(\rho _0\) is a constant. The electric field at an internal point \((r < R)\) is

JEE Mains 2014 Hard
The elastic limit of brass is \(379\,MPa.\) .......... \(mm\) should be the minimum diameter of a brass rod if it is to support a \(400\,N\) load without exceeding its elastic limit .

JEE Mains 2019 Medium
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason \(R\) Assertion \(A:\) The beam of electrons shows wave nature and exhibit interference and diffraction. Reason \(R\) : Davisson Germer Experimentally verified the wave nature of electrons. In the light of the above statements. Choose the most appropriate answer from the options given below :

JEE Mains 2023 Medium
A gas is compressed from a volume of \(2\,m^3\) to a volume of \(1\, m^3\) at a constant pressure of \(100\, N/m^2\). Then it is heated at constant volume by supplying \(150\, J\) of energy. As a result, the internal energy of the gas

JEE Mains 2014 Medium

Explore more questions on app

From JEE Mains

Two particles are located at equal distance from origin. The position vectors of those are represented by \(\bar{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k}\) and \(\bar{B}=2 \hat{i}-2 \hat{j}+4 p \hat{k}\), respectively. If both the vectors are at right angle to each other, the value of \(\mathrm{n}^{-1}\) is _____ .

JEE Mains 2025 Medium
A potentiometer wire of length \(10 \,m\) and resistance\(20 \,\Omega\) is connected in series with a \(25 \,V\) battery and an external resistance \(30\, \Omega\). A cell of emf \(E\) in secondary circuit is balanced by \(250\, cm\) long potentiometer wire. The value of \(E\) (in volt) is \(\frac{x}{10}\). The value of \(x\) is.......

JEE Mains 2022 Medium
Two identical cells each of emf \(1.5\,V\) are connected in series across a \(10\,\Omega\) resistance. An ideal voltmeter connected across \(10\,\Omega\) resistance reads \(1.5\,V\). The internal resistance of each cell is \(......\Omega\).

JEE Mains 2023 Medium
Energy of \(10\) non rigid diatomic molecules at temperature \(\mathrm{T}\) is _______.

JEE Mains 2024 Hard

Explore more questions on app