JEE Physics 2025 Question with Solution

Given: Assertion $A$ states that a sound wave has higher speed in solids than in gases. Reason $R$ states that gases have higher value of Bulk modulus than solids.

Find: Determine which option correctly describes the truth of $A$ and $R$.

The speed of sound in a medium is given by

where $B$ is the bulk modulus and $\rho$ is the density of the medium.

In solids, the value of bulk modulus is very high, so solids resist compression much more strongly than gases. Therefore, sound travels faster in solids than in gases. Hence, Assertion $A$ is true.

The statement in Reason $R$ is incorrect because gases do not have higher bulk modulus than solids. In fact, solids generally have a much higher bulk modulus than gases. Hence, Reason $R$ is false.

Therefore, the correct option is D.

Given: Two statements are provided as Assertion $A$ and Reason $R$.

Find: Check the correctness of both statements.

1. Evaluate Assertion $A$. Sound travels faster in solids than in gases because solids are much more rigid and have stronger elastic properties.

2. Evaluate Reason $R$. The reason says that gases have higher bulk modulus than solids. This is false because solids generally have much higher bulk modulus, while gases are highly compressible.

3. Conclude. Since Assertion $A$ is true and Reason $R$ is false, the correct choice is $A$ is true but $R$ is false.

Therefore, the correct option is D.