
The assertion correctly defines the property of elasticity. The reason explains that the restoring force is a result of interatomic and intermolecular forces, which is true. However, while the reason is accurate, it does not necessarily explain the assertion in all contexts.
The Correct answer is: Both (A) and (R) are true and (R) is the correct explanation (A)
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 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 .
Let the domain of the function \( f(x) = \log_{2} \log_{4} \log_{6}(3 + 4x - x^{2}) \) be \( (a, b) \). If \[ \int_{0}^{b-a} [x^{2}] \, dx = p - \sqrt{q} - \sqrt{r}, \quad p, q, r \in \mathbb{N}, \, \gcd(p, q, r) = 1, \] where \([ \, ]\) is the greatest integer function, then \( p + q + r \) is equal to