Let's analyze each statement separately in terms of the physics concepts they involve:
Combining both analyses, we find that Statement I is incorrect whereas Statement II is correct. Therefore, the most appropriate choice is:
The correct answer is: Statement I is incorrect but Statement II is correct.
Step 1. Analysis of Statement (I): - Viscosity is a measure of a fluid’s resistance to flow. Generally, liquids have higher viscosity than gases because of stronger intermolecular forces in liquids. Therefore, Statement (I) is incorrect.
Step 2. Analysis of Statement (II): - Surface tension is influenced by impurities. Insoluble impurities generally decrease the surface tension of a liquid by disrupting cohesive forces at the surface. Thus, Statement (II) is correct.
Since Statement I is incorrect and Statement II is correct, the correct answer is (2).
Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all \( x, y \in \mathbb{R}. \)
If \( f'(0) = \frac{1}{2} \), then the value of \( 24f''\left( \frac{5\pi}{3} \right) \) is: