Two identical particles each of mass m are in | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The reduced mass of the system is given by:$\mu = \frac{m_1 m_2}{m_1 + m_2} = \frac{m \cdot m}{m + m} = \frac{m^2}{2m} = \frac{m}{2}$The given sys

Vedclass · Accepted Answer

$\pi \sqrt {\frac{{2m}}{k}} $

Vedclass · Answer

(D) The reduced mass of the system is given by:$\mu = \frac{m_1 m_2}{m_1 + m_2} = \frac{m \cdot m}{m + m} = \frac{m^2}{2m} = \frac{m}{2}$The given system of two particles connected by a spring is equivalent to a single particle of mass $\mu$ connected to a fixed wall by a spring of stiffness $k$.The time period of oscillation for this equivalent system is:$T = 2\pi \sqrt{\frac{\mu}{k}}$Substituting the value of $\mu = \frac{m}{2}$:$T = 2\pi \sqrt{\frac{m/2}{k}} = 2\pi \sqrt{\frac{m}{2k}} = 2\pi \frac{1}{\sqrt{2}} \sqrt{\frac{m}{k}} = \sqrt{2} \cdot \sqrt{2} \pi \sqrt{\frac{m}{2k}} = \pi \sqrt{\frac{4m}{2k}} = \pi \sqrt{\frac{2m}{k}}$Thus,the correct option is $D$.

Two identical particles each of mass $m$ are interconnected by a light spring of stiffness $k$. The time period for small oscillations is equal to:

Similar Questions

Two masses $m_1$ and $m_2$ are suspended together by a massless spring of constant $k$. When the masses are in equilibrium,$m_1$ is removed without disturbing the system. Then the angular frequency of oscillation of $m_2$ is

The restoring force of a spring with a block attached to the free end of the spring is represented by

When a mass $m$ is connected individually with two springs $S_1$ and $S_2$,the oscillation frequencies are $n_1$ and $n_2$. If the mass $m$ is attached to the springs as shown in the figure,the oscillation frequency would be

$A$ body of mass $4 \ kg$ attached to a spring of force constant $64 \ N \ m^{-1}$ executes simple harmonic motion on a frictionless horizontal surface. The time period of oscillation is

Two masses $m_1$ and $m_2$ connected by a spring of spring constant $k$ rest on a frictionless surface. If the masses are pulled apart and let go,the time period of oscillation is

Vedclass Test Series

Exam Paper Generator

Online Exam Module