Two masses m₁=1 ,kg and m₂=0.5 ,kg are suspended together by a massless spring of spring constan

English

Gujarati

Hindi

13.Oscillations

medium

Two masses $m_1=1 \,kg$ and $m_2=0.5 \,kg$ are suspended together by a massless spring of spring constant $12.5 \,Nm ^{-1}$. When masses are in equilibrium $m_1$ is removed without disturbing the system. New amplitude of oscillation will be .......... $cm$

A

$30$

B

$50$

C

$80$

D

$60$

Solution

(c)

Points of equilibrium of the spring will be when no force acts on it.

$k x=\left(m_1+m_2\right) g$

$x=\frac{\left(m_1+m_2\right) g}{k}$

The new equilibrium position which will be the mean position of $S.H.M.$ will be simply $\frac{m_2 g}{k}$

New amplitude will be maximum displacement from $\frac{m_2 g}{k}$ which is :

$A=\frac{\left(m_1+m_2\right) g}{k}-\frac{m_2 g}{k}$

or $A=\frac{m_1 g}{k}$

or $A=\frac{1 \times 10}{12.5}$

or $A=\frac{4}{5} \,m$

$\therefore A=0.8 \,m$ or $80 \,cm$

Standard 11

Physics

Share

Similar Questions

A mass of $0.2\,kg$ is attached to the lower end of a massless spring of force-constant $200\, N/m,$ the upper end of which is fixed to a rigid support. Which of the following statements is/are true ?

normal

Two bodies of masses $1\, kg$ and $4\, kg$ are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency $25\, rad/s$, and amplitude $1.6\, cm$ while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is ….. $N$ ( take $g = 10\, ms^{-2}$)

hard

(JEE MAIN-2014)

Find the ratio of time periods of two identical springs if they are first joined in series $\&$ then in parallel $\&$ a mass $m$ is suspended from them :

medium

As per given figures, two springs of spring constants $K$ and $2\,K$ are connected to mass $m$. If the period of oscillation in figure $(a)$ is $3 s$, then the period of oscillation in figure $(b)$ will be $\sqrt{ x }$ s. The value of $x$ is$………$

medium

(JEE MAIN-2022)

Is the following Statement True or False ?

$1.$ If the spring is cut in two equal piece the spring constant of every piece decreases.

$2.$ Displacement of $SHO$ increases, its acceleration decrease.

$3.$ A system can happen to oscillate, have more than one natural frequency.

$4.$ The periodic time of $SHM$ depend on amplitude or energy or phase constant.

medium