A spring has spring constant $k$ and $l$. If it cut into piece spring in the proportional to $\alpha : \beta : \gamma $ then obtain the spring constant of every piece in term of spring constant of original spring (Here, $\alpha $, $\beta $ and $\gamma $ are integers)
A block of mass $2\,kg$ is attached with two identical springs of spring constant $20\,N / m$ each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is $\frac{\pi}{\sqrt{x}}$ in SI unit. The value of $x$ is $..........$
A block $P$ of mass $m$ is placed on a smooth horizontal surface. A block $Q$ of same mass is placed over the block $P$ and the coefficient of static friction between them is ${\mu _S}$. A spring of spring constant $K$ is attached to block $Q$. The blocks are displaced together to a distance $A$ and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the block is
In arrangement given in figure, if the block of mass m is displaced, the frequency is given by
A weightless spring of length $60\, cm$ and force constant $200\, N/m$ is kept straight and unstretched on a smooth horizontal table and its ends are rigidly fixed. A mass of $0.25\, kg$ is attached at the middle of the spring and is slightly displaced along the length. The time period of the oscillation of the mass is