A cantilever of length 2 cm and depth 10 cm tapers in plan from a width 24 cm to zero at its free end. If the modulus of elasticity of the material is 0.2 × 106 N/mm2, the deflection of the free end, is A. 2 mm B. 3 mm C. 4 mm D. 5 mm

The correct answer is $\boxed{\text{B) 3 mm}}$.

The deflection of a cantilever beam is given by the following formula:

$$\delta = \frac{FL^3}{3EI}$$

where:

• $\delta$ is the deflection,
• $F$ is the applied force,
• $L$ is the length of the beam,
• $E$ is the modulus of elasticity, and
• $I$ is the moment of inertia.

The moment of inertia of a cantilever beam with a uniform cross-section is given by the following formula:

$$I = \frac{bh^3}{12}$$

where:

• $b$ is the width of the beam,
• $h$ is the depth of the beam.

In this case,