List of top Physics Questions on Elasticity asked in JEE Main

A spring of spring constant K = 15 N/m is cut into two parts of ratio of length 3 : 1. Find the spring constant of spring with smaller length (in N/m).
A spring of force constant $15\,\text{N/m}$ is cut into two pieces. If the ratio of their lengths is $1:3$, then the force constant of the smaller piece is ___ $\text{N/m}$.
If percentage increase in Young's modulus \(Y\) is \(1%\), percentage increase in density of material is \(0.5%\) and longitudinal wave traveling in a metallic bar has wave velocity of \(400\,\text{m/s}\), then find final velocity of the wave.

\( x \) is a peptide which is hydrolyzed to 2 amino acids \( y \) and \( z \). \( y \) when reacted with HNO\(_2\) gives lactic acid. \( z \) when heated gives a cyclic structure as below: 

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of 0.8 cm$^3$. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ______ litre. (Take 1 atm = $10^5$ Pa)
The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N, the length of the string is 1.56 m. The original length of the string is ______ m.

A steel wire of length 2 m and Young's modulus \( 2.0 \times 10^{11} \, \text{N/m}^2 \) is stretched by a force. If Poisson's ratio and transverse strain for the wire are \( 0.2 \) and \( 10^{-3} \) respectively, then the elastic potential energy density of the wire is \( \times 10^6\), in SI units .

Two slabs with square cross section of different materials $(1,2)$ with equal sides $(l)$ and thickness $\mathrm{d}_{1}$ and $\mathrm{d}_{2}$ such that $\mathrm{d}_{2}=2 \mathrm{~d}_{1}$ and $l>\mathrm{d}_{2}$. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is $\theta_{2}=2 \theta_{1}$. If the shear moduli of material 1 is $4 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$, then shear moduli of material 2 is $\mathrm{x} \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$, where value of x is _______ .

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of $ 10^5 $ N at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement $ \theta $ of the rod axis from its original position would be: (shear moduli $ G = 10^{10} $ N/m$^2$)
One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of the upper wire to that of the lower wire will be:\[\text{[Area of cross section of wire = 0.005 cm}^2, \, Y = 2 \times 10^{11} \, \text{N/m}^2, \, g = 10 \, \text{m/s}^2\text{]}\]
A wire of cross-sectional area $A$, modulus of elasticity $2 \times 10^{11} \, \text{Nm}^{-2}$, and length $2 \, \text{m}$ is stretched between two vertical rigid supports.
When a mass of $2 \, \text{kg}$ is suspended at the middle, it sags lower from its original position making angle $\theta = \frac{1}{100}$ radian on the points of support.  
The value of $A$ is ____ $\times 10^{-4} \, \text{m}^2$ (consider $x \ll l$).  
(Given: $g = 10 \, \text{m/s}^2$)
wire and mass
The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is :
With rise in temperature, the Young's modulus of elasticity
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity.
Reason (R) : The restoring force depends upon the bonded inter atomic and inter molecular force of solid.
In the light of the above statements, choose the correct answer from the options given below :
Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are $Y_1$ and $Y_2$. The combination behaves as a single wire then its Young's modulus is :
A uniform heavy rod of weight \(10\,\text{kg}\,\text{ms}^{-2}\), cross-sectional area \(100\,\text{cm}^2\) and length \(20\,\text{cm}\) is hanging from a fixed support. Young modulus of the material of the rod is \(2 \times 10^{11}\,\text{Nm}^{-2}\). Neglecting the lateral contraction, find the elongation of rod due to its own weight :
If Y, K and η are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.
Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a : b. Then a/b can be expressed as 1/x where x is __________.