Draw the force-displacement graph for a spring.

A mass $m$ is attached to two springs as shown in figure. The spring constants of two springs are $K_1$ and $K_2.$ For the frictionless surface, the time period of oscillation of mass $m$ is

The two blocks $P$ and $Q$ are connected by a metal wire with breaking stress ${10}^9 \mathrm{N} {\mathrm{m}}^{-2}$ through a frictionless pulley. The minimum radius of the wire for it not to break is (consider $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

As shown in the figure, an iron block $A$ of volume $0.25 {\mathrm{m}}^3$ is attached to a spring $S$ of unstretched length $1.0 \mathrm{m}$ and hanging to the ceiling of a roof. The spring gets stretched by $0.2 \mathrm{m}$. This block is removed and another block $B$ of iron of volume $0.75 {\mathrm{m}}^3$ is now attached to the same spring and kept on a frictionless incline plane of $30°$ inclination. The distance of the block from the top along the incline at equilibrium is

Two identical springs are connected to mass$m$ as shown $(k=\text{spring constant})$ . If the period of the configuration in (i) is $2 \mathrm{s}$, the period of the configuration (ii) is:

I 

II 

A block of mass $20 \mathrm{kg}$ is suspended through two spring balances with negligible mass as shown in figure. What will be the readings in the upper and lower balance respectively ?

Two blocks, $A$ and $B$ of masses, $2m$ and $m$, respectively, are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of $A$ and $B$, immediately after the string is cut, respectively are

Area of piston is 1 m². When heat is supplied to the gas it expands and displaces piston by $\frac{\text{L}}{2}$ where L = 1m. Natural length of springs is L = 1m. Spring constant K = 100 N/m. The pressure of gas in final situation is –