Physics Q24 – NEET-UG 2026

Home Physics Thermal PropertiesQuestion #496

The temperature of a metallic sphere of radius

R

is increased by a small amount

Δ T

. If the linear coefficient of thermal expansion of the metal is

α

, the approximate increase in the volume of the sphere is :

Clue 1 of 3: Thermal Expansion

Understand the concept of thermal expansion, which describes how the dimensions of a material change with temperature.

🧠 Full Solution Path

Step 1: Identify Initial Volume and Expansion Coefficients✦ Active

The initial volume of a sphere with radius $R$ is given by the formula $V = \frac{4}{3} π R^{3}$ . The problem states that the linear coefficient of thermal expansion is $α$ . For small temperature changes in isotropic materials, the coefficient of volume expansion $γ$ is related to the linear coefficient $α$ by the relation $γ = 3 α$ .

Step 2: Apply Volume Expansion Formula○ Expand

The approximate increase in volume $Δ V$ due to a temperature change $Δ T$ is given by the formula for volume expansion:

Δ V = V γ Δ T

Step 3: Substitute and Calculate○ Expand

Substitute the expressions for $V$ and $γ$ into the volume expansion formula:

Δ V = (\frac{4}{3} π R^{3}) (3 α) Δ T

Simplifying the expression, we get:

Δ V = 4 π R^{3} α Δ T

💡 Teacher's Secret Hint

Remember that the relationship $γ = 3 α$ is an approximation valid for small temperature changes.

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Physics Question 24 – NEET-UG 2026

Clue 1 of 3: Thermal Expansion

🧠 Full Solution Path