Assuming all pulleys, springs and string massless. Consider all surface smooth. Choose the correct statement $(s)$
Assuming all pulleys, springs and string massless. Consider all surface smooth. Choose the correct statement $(s)$
- A
The angular frequency for small oscillation of the system is $\sqrt \frac{K}{3m}$
- B
The angular frequency for small oscillation of the system is $\sqrt \frac{4K}{33m}$
- C
The elastic potential energy of system at equilibrium is $\frac{33m^2g^2}{4K}$
- D
The elastic potential energy of system at equilibrium is $\frac{3m^2g^2}{2K}$
Similar Questions
The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended , the period of oscillation will now be
The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended , the period of oscillation will now be
- [AIPMT 2010]
Two identical balls A and B each of mass 0.1 kg are attached to two identical massless springs. The spring mass system is constrained to move inside a rigid smooth pipe bent in the form of a circle as shown in the figure. The pipe is fixed in a horizontal plane. The centres of the balls can move in a circle of radius 0.06 m. Each spring has a natural length of 0.06$\pi$ m and force constant 0.1N/m. Initially both the balls are displaced by an angle $\theta = \pi /6$ radian with respect to the diameter $PQ$ of the circle and released from rest. The frequency of oscillation of the ball B is
Two identical balls A and B each of mass 0.1 kg are attached to two identical massless springs. The spring mass system is constrained to move inside a rigid smooth pipe bent in the form of a circle as shown in the figure. The pipe is fixed in a horizontal plane. The centres of the balls can move in a circle of radius 0.06 m. Each spring has a natural length of 0.06$\pi$ m and force constant 0.1N/m. Initially both the balls are displaced by an angle $\theta = \pi /6$ radian with respect to the diameter $PQ$ of the circle and released from rest. The frequency of oscillation of the ball B is
Springs of spring constants $K, 2K, 4K, 8K,$ ..... are connected in series. A mass $40\, gm$ is attached to the lower end of last spring and the system is allowed to vibrate. What is the time period of oscillation ..... $\sec$. (Given $K = 2\, N/cm$)
Springs of spring constants $K, 2K, 4K, 8K,$ ..... are connected in series. A mass $40\, gm$ is attached to the lower end of last spring and the system is allowed to vibrate. What is the time period of oscillation ..... $\sec$. (Given $K = 2\, N/cm$)
Two pendulums have time periods $T$ and $\frac{{5T}}{4}.$They start $S.H.M.$ at the same time from the mean position. What will be the phase difference between them after the bigger pendulum has complete one oscillation ..... $^o$
Two pendulums have time periods $T$ and $\frac{{5T}}{4}.$They start $S.H.M.$ at the same time from the mean position. What will be the phase difference between them after the bigger pendulum has complete one oscillation ..... $^o$
If the period of oscillation of mass $m$ suspended from a spring is $2\, sec$, then the period of mass $4m$ will be .... $\sec$
If the period of oscillation of mass $m$ suspended from a spring is $2\, sec$, then the period of mass $4m$ will be .... $\sec$
- [AIIMS 1998]