JEE Main · Physics ↓ Falling

Mechanical Properties of Solids appeared 21 times across 3 years — 2.4% of Physics. This question is from Elastic Moduli.

Year 2026 2025 2024 Total
Questions 4 9 8 21

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of 10⁵ N at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement θ of the rod axis from its original position would be : (shear moduli, G=10¹⁰ N/m²)

Solution & Explanation

Related Formula
G = σshearθ = (F)/(A · θ)

where A = π r² is the cross-sectional area.

Core Logic

Rearranging the formula for θ:

θ = (F)/(A · G) = (F)/(π r² · G)

Substituting the values:

F = 10⁵ N r = 4 cm = 4 × 10⁻² m G = 10¹⁰ N/m²
Step 1: Calculate Angular Displacement
θ = 10⁵π × (4 × 10⁻²)² × 10¹⁰ θ = 10⁵π × 16 × 10⁻⁴ × 10¹⁰ = (10⁵)/(16π × 10⁶) θ = (1)/(160π) radians
Pattern Recognition

Shear strain definition is straightforwardly matching the geometry angle of shift. Avoid radius-to-diameter or unit mismatches.

Chapter Mix

Class 11 Physics: Mechanical Properties of Solids

Shear stress configuration on vertical rod
Shear stress configuration on vertical rod

Reference Study Guides

More Mechanical Properties of Solids Previous-Year Questions — Page 5

Q58 jee_main_2024_31_jan_morning Bulk Modulus
The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.02% is ________ m. (Take density of sea water = 10³ kgm⁻³, Bulk modulus of rubber = 9 × 10⁸ Nm⁻², and g = 10 ms⁻²)
Numerical Answer. Answer: 18 to 18

Solution

Related Formula
β = (-Δ P)/((Δ V)/(V)) Δ P = ρ g h
Core Logic

The change in pressure Δ P is the hydrostatic pressure at depth h.

Δ P = -β (Δ V)/(V) ρ g h = -β (Δ V)/(V)
Step 2: Calculation

Given values: ρ = 10³ kg/m³ g = 10 m/s² β = 9 × 10⁸ N/m² (Δ V)/(V) = -0.02% = -(0.02)/(100)

Substitute into the equation:

10³ × 10 × h = - (9 × 10⁸) × (-(0.02)/(100)) 10⁴ × h = 9 × 10⁸ × 2 × 10⁻⁴ 10⁴ h = 18 × 10⁴ h = 18 m
Chapter Mix

Class 11 Physics: Mechanical Properties Of Solids Class 11 Physics: Mechanical Properties Of Fluids

More Mechanical Properties of Solids Questions — jee_main_2025_04_april_evening

Practice all Mechanical Properties of Solids previous-year questions →

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JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)