What does the slope of a force vs displacement graph represent?

when their lengths are increased by the same amount,

The tension in the given spring is

Two wires of equal length and cross-section area are suspended as shown in the figure. Their Young's modulus are $Y_1$ and $Y_2$, respectively. The equivalent Young's modulus will be

A metal wire of length $L_1$ and area of cross section A is attached to a rigid support. Another metal wire of length $L_2$ and of the same cross-sectional area is attached to free end of the first wire. A body of mass $\mathrm{M}$ is then suspended from the free end of the second wire. If $Y_1$ and $Y_2$ are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

when they are stretched by the same force ?

A massless spring balance is attached to $2 \mathrm{kg}$ trolley and is used to pull the trolley along a flat surface as shown in the figure. The reading on the spring balance remains at $10 \mathrm{kg}$ during the motion. The acceleration of the trolley is: $\left(g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

The extensions for different loads are given in the table.

Copy and complete the sentence by the inserting the appropriate word.

Within the limits of experimental accuracy, the load, the load and the extension of the spring are _____ to each other.

An ideal spring, with a pointer attached to its end, hangs next to a scale. With $100\mathrm{ }\mathrm{N}$ weight attached and in equilibrium, the pointer indicates $40$ on the scale, as shown. Using a $200\mathrm{ }\mathrm{N}$ weight instead results in $60$ on the scale. Using an unknown weight $X$ instead results in $30$ on the scale. Find the value of $X$.