Rigidity Modulu PYQs: JEE Mains Physics

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1. 1. A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of \(10^5 \mathrm{~N}\) 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, \(\left.\mathrm{G}=10^{10} \mathrm{~N} / \mathrm{m}^2\right)\) 2025 Medium
2. 2. 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. 2025 Medium
3. 3. 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 \(l \gt \mathrm{d}_2\). 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 ________. 2025 Hard
4. 4. A square aluminium (shear modulus is \(25 \times 10^{9}\,Nm ^{-2}\) ) slab of side \(60\,cm\) and thickness \(15\,cm\) is subjected to a shearing force (on its narrow face) of \(18.0 \times 10^{4}\,N\). The lower edge is riveted to the floor. The displacement of the upper edge is \(.......\mu\,m\). 2022 Hard

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