Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 2011
Exam
JEE Main
Year
2011
Subject
Physics
Chapter
Oscillations

JEE Main 2011 · Physics · Oscillations

A mass M , attached to a horizontal spring, executes S.H.M. with...

A mass MM, attached to a horizontal spring, executes S.H.M. with amplitude A1A_1. When the mass MM passes through its mean position then a smaller mass m\mathrm{m} is placed over it and both of them move together with amplitude A2A_2. The ratio of (A1A2)\left(\frac{A_1}{A_2}\right) is :

Options

  1. AM+mM\frac{M+m}{M}
  2. B(MM+m)1/2\left(\frac{M}{M+m}\right)^{1 / 2}
  3. C(M+mM)1/2\left(\frac{\mathrm{M}+\mathrm{m}}{\mathrm{M}}\right)^{1 / 2}
  4. DMM+m\frac{M}{M+m}

Correct answer

C. (M+mM)1/2\left(\frac{\mathrm{M}+\mathrm{m}}{\mathrm{M}}\right)^{1 / 2}

Step-by-step solution

Energy of simple harmonic oscillator is constant. ⇒12Mω2A12=12(m+M)ω2A22A12A22=M+mM∴A1A2=M+mM\begin{aligned}& \Rightarrow \frac{1}{2}M \omega^2 A_1^2=\frac{1}{2}(m+M) \omega^2 A_2^2 \\ & \frac{A_1^2}{A_2^2}=\frac{M+m}{M}\\ & \therefore \frac{A_1}{A_2}=\sqrt{\frac{M+m}{M}} \end{aligned}
Practice Oscillations on Quantrex Academy →

More from Oscillations

A tank contains two immiscible liquids of densities 6ρ and 2ρ . The higher density liquid… JEE Advanced 2026The frequency of oscillation of a mass m suspended by a spring is v_1 . If the length of… JEE Main 2026A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium… JEE Main 2026A particle is executing simple harmonic motion. Its amplitude is A and time period is 5… JEE Main 2026Match List-I with List-II. List-I List-II A. ^2 ω t I. Periodic with time period T =… JEE Main 2026A uniform disc of radius R and mass M is free to oscillate about the axis A as shown in… JEE Main 2026The velocity of a particle executing simple harmonic motion along x -axis is described as… JEE Main 2026The equation of motion of a particle is given by x = a (50t + (π)/(3)) cm. The particle… JEE Main 2026 Full Oscillations list All JEE Main PYQs