A uniform rod of length $2.0 \,m$ is suspended through an end and is set into oscillation with small amplitude under gravity. The time period of oscillation is approximately .... $\sec$
Medium
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Column $I$ describe some situations in which a small object moves. Column $II$ describes some characteristics of these motions. Match the situation in Column $I$ with the characteristics in Column $II$ and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.View Solution
Column $I$ Column $II$ $(A)$ The object moves on the $\mathrm{x}$-axis under a conservative force in such a way that its "speed" and "position" satisfy $v=c_1 \sqrt{c_2-x^2}$, where $\mathrm{c}_1$ and $\mathrm{c}_2$ are positive constants. $(p)$ The object executes a simple harmonic motion. $(B)$ The object moves on the $\mathrm{x}$-axis in such a way that its velocity and its displacement from the origin satisfy $\mathrm{v}=-\mathrm{kx}$, where $\mathrm{k}$ is a positive constant. $(q)$ The object does not change its direction. $(C)$ The object is attached to one end of a massless spring of a given spring constant. The other end of the spring is attached to the ceiling of an elevator. Initially everything is at rest. The elevator starts going upwards with a constant acceleration a. The motion of the object is observed from the elevator during the period it maintains this acceleration. $(r)$ The kinetic energy of the object keeps on decreasing. $(D)$ The object is projected from the earth's surface vertically upwards with a speed $2 \sqrt{\mathrm{GM}_e / R_e}$, where, $M_e$ is the mass of the earth and $R_e$ is the radius of the earth. Neglect forces from objects other than the earth. $(s)$ The object can change its direction only once. - 2Consider a one-dimensional potential $V(x)$ as shown in the figure below. A classical particle of mass $m$ moves under its influence and has total energy $E$ as shown below. The motion isView Solution
- 3When a mass $M$ is attached to the spring of force constant $k$, then the spring stretches by $l$. If the mass oscillates with amplitude $l$, what will be maximum potential energy stored in the springView Solution
- 4A particle executes simple harmonic motion with a frequency $f$. The frequency with which its kinetic energy oscillates isView Solution
- 5A particle moves such that its acceleration $a$ is given by $a = - bx$, where $x$ is the displacement from equilibrium position and b is a constant. The period of oscillation isView Solution
- 6View SolutionThe total energy of a particle, executing simple harmonic motion is
- 7A vertical mass-spring system executes simple harmonic oscillations with a period of $2\,s$. A quantity of this system which exhibits simple harmonic variation with a period of $1\, s$ isView Solution
- 8Dispacement time graph of a particle executing $SHM$ is as shown in the figure. Corresponding graph between $PE$ and time isView Solution
- 9Consider the following statements. The total energy of a particle executing simple harmonic motion depends on itsView Solution
$(1)$ Amplitude $(2) $ Period $(3)$ Displacement
Of these statements
- 10A solid cylinder of density $\rho_0$, cross-section area $A$ and length $l$ floats in a liquid $\rho(> \rho_0)$ with its axis vertical, as shown. If it is slightly displaced downward and released, the time period will beView Solution
