A mass 0.9 , kg,attached to a horizontal spri | vedclass

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

Question

(C) The total energy of the $SHM$ is given by $E = \frac{1}{2} k A^2$. At the mean position,the potential energy is zero,so the total energy is purely

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(C) The total energy of the $SHM$ is given by $E = \frac{1}{2} k A^2$. At the mean position,the potential energy is zero,so the total energy is purely kinetic: $E = \frac{p^2}{2m}$,where $p$ is the momentum.Since the mass is added at the mean position,the velocity $v$ changes,but the momentum $p$ is conserved during the instantaneous placement of the mass.Initial mass $m_1 = 0.9 \, kg = 900 \, g$. Final mass $m_2 = 900 \, g + 124 \, g = 1024 \, g$.Since $E = \frac{1}{2} k A^2 = \frac{p^2}{2m}$,we have $A \propto \frac{1}{\sqrt{m}}$ for a constant momentum $p$.Therefore,$\frac{A_1}{A_2} = \sqrt{\frac{m_2}{m_1}} = \sqrt{\frac{1024}{900}} = \frac{32}{30} = \frac{16}{15}$.Given $\frac{A_1}{A_2} = \frac{\alpha}{\alpha-1} = \frac{16}{16-1}$.Comparing the terms,we get $\alpha = 16$.

Similar Questions

$A$ particle of mass $200 \,g$ executes $S.H.M.$ The restoring force is provided by a spring of force constant $80 \,N/m$. The time period of oscillations is .... $s$.

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $K_{1}$ and $K_{2}$ respectively. If the maximum velocities during oscillations are equal,the ratio of the amplitude of $A$ and $B$ is

$A$ flat horizontal board moves up and down in $S.H.M.$ vertically with amplitude $A$. The shortest permissible time period of the vibration such that an object placed on the board may not lose contact with the board is ..........

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 a spring constant $k,$ the frequency of oscillation of the given body is:

$A$ particle of mass $200\,g$ executes a simple harmonic motion. The restoring force is provided by a spring of spring constant $80\,N/m$. The time period is .... $\sec$

Vedclass Test Series

Exam Paper Generator

Online Exam Module