Two springs with spring constants ${K_1} = 1500\,N/m$ and ${K_2} = 3000\,N/m$ are stretched by the same force. The ratio of potential energy stored in spring will be
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A simple pendulum suspended from the ceiling of a stationary lift has period $T_0$. When the lift descends at steady speed, the period is $T_1$, and when it descends with constant downward acceleration, the period is $T_2$. Which one of the following is true?
A clock $S$ is based on oscillations of a spring and a clock $P$ is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having same density as earth but twice the radius then
An oscillator of mass $M$ is at rest in its equilibrium position in a potential $V\, = \,\frac{1}{2}\,k{(x - X)^2}.$ A particle of mass $m$ comes from right with speed $u$ and collides completely inelastically with $M$ and sticks to it . This process repeats every time the oscillator crosses its equilibrium position .The amplitude of oscillations after $13$ collisions is: $(M = 10,\, m = 5,\, u = 1,\, k = 1 ).$
If $A$ is the area of cross-section of a spring $L$ is its length $E$ is the Young's modulus of the material of the spring then time period and force constant of the spring will be respectively
A system of two identical rods ($L-$ shaped) of mass $m$ and length $l$ are resting on a peg $P$ as shown in the figure. If the system is displaced in its plane by a small angle $\theta ,$ find the period of oscillations :