Physics Q94 – AP-EAMCET 2026

Home Physics Mechanical Properties of SolidsQuestion #281

A book of dimension

4 cm \times 1.5 cm \times 10 cm

is kept in a way that the

10 cm

edge is vertical. A horizontal force of

3 N

is applied at the top face. If the shear modulus of the book is

2 \times 10^{5} {Nm}^{- 2}

, then the horizontal displacement of the top face will be

Clue 1 of 3: Understanding Shear Deformation

When a tangential force is applied to the surface of an object, it causes a deformation where layers of the object slide past each other, resulting in a change in shape without a change in volume.

🧠 Full Solution Path

Step 1: Identify Relevant Parameters and Convert Units✦ Active

The book's dimensions are $4 cm \times 1.5 cm \times 10 cm$ . The $10 cm$ edge is vertical, which means it is the height ( $L$ ) over which the shear deformation occurs. The horizontal force is applied to the top face, so the area ( $A$ ) on which the force acts is formed by the other two dimensions. The given force is $F = 3 N$ and the shear modulus is $G = 2 \times 10^{5} {Nm}^{- 2}$ . It is crucial to convert all dimensions to meters for consistency in units.

L = 10 cm = 0.1 m

A = 4 cm \times 1.5 cm = 6 {cm}^{2} = 6 \times (10^{- 2} m)^{2} = 6 \times 10^{- 4} m^{2}

The force is $F = 3 N$ and the shear modulus is $G = 2 \times 10^{5} {Nm}^{- 2}$ .

💡 Teacher's Secret Hint

Always ensure all physical quantities are in consistent SI units (meters, kilograms, seconds) before performing calculations to avoid errors.

Step 2: Recall the Formula for Shear Modulus and Shear Strain○ Expand

The shear modulus ( $G$ ) is a measure of an object's resistance to shear deformation. It is defined as the ratio of shear stress ( $τ$ ) to shear strain ( $γ$ ).

G = \frac{Shear Stress}{Shear Strain} = \frac{τ}{γ}

Shear stress is the tangential force ( $F$ ) applied per unit area ( $A$ ), and shear strain is the ratio of the horizontal displacement ( $Δ x$ ) to the original height ( $L$ ).

τ = \frac{F}{A}

γ = \frac{Δ x}{L}

Substituting these into the shear modulus formula gives:

G = \frac{F / A}{Δ x / L} = \frac{F \cdot L}{A \cdot Δ x}

💡 Teacher's Secret Hint

Remember that shear stress is caused by a tangential force, not a normal force. Shear strain is a dimensionless quantity.

Step 3: Rearrange the Formula to Solve for Horizontal Displacement○ Expand

Our goal is to find the horizontal displacement ( $Δ x$ ). We can rearrange the shear modulus formula to isolate $Δ x$ :

G = \frac{F \cdot L}{A \cdot Δ x} ⟹ Δ x = \frac{F \cdot L}{A \cdot G}

💡 Teacher's Secret Hint

Algebraic manipulation is a common source of error. Double-check your rearrangement to ensure the desired variable is correctly isolated.

Step 4: Substitute Values and Calculate Displacement○ Expand

Now, substitute the values identified in Step 1 into the rearranged formula for $Δ x$ :

Δ x = \frac{3 N \times 0.1 m}{(6 \times 10^{- 4} m^{2}) \times (2 \times 10^{5} {Nm}^{- 2})}

Δ x = \frac{0.3}{12 \times 10^{1}} = \frac{0.3}{120}

Δ x = \frac{3}{1200} = \frac{1}{400} m

Δ x = 0.0025 m

💡 Teacher's Secret Hint

Pay close attention to powers of ten during calculation. A common mistake is misplacing the decimal point or incorrectly handling exponents.

Step 5: Convert to Millimeters and Select the Correct Option○ Expand

The calculated displacement is in meters. The options are given in millimeters, so we need to convert the result:

Δ x = 0.0025 m \times \frac{1000 mm}{1 m} = 2.5 mm

This value matches option 2.

💡 Teacher's Secret Hint

Always check the units of the options provided. Often, the calculated answer needs a final unit conversion to match the options.

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Physics Question 94 – AP-EAMCET 2026

Clue 1 of 3: Understanding Shear Deformation

🧠 Full Solution Path