Given below are two statements: one is labelled as Assertion \(A\) and the other as Reason \(R\):
Assertion \(A\): A sound wave has higher speed in solids than in gases.
Reason \(R\): Gases have higher value of Bulk modulus than solids.
Step 1: Evaluate the truth of \(A\) and \(R\). Sound travels faster in solids than in gases due to the higher density and elastic properties of solids, not gases.
Step 2: Determine the correctness of \(R\). In fact, solids generally have a higher Bulk modulus than gases, contradicting the statement of \(R\).
Conclusion: Assertion \(A\) is true, stating that sound waves travel faster in solids is correct, but Reason \(R\) is false as gases typically have a lower Bulk modulus than solids.
A cube of side 10 cm is suspended from one end of a fine string of length 27 cm, and a mass of 200 grams is connected to the other end of the string. When the cube is half immersed in water, the system remains in balance. Find the density of the cube.
In a low-speed airplane, a venturimeter with a 1.3:1 area ratio is used for airspeed measurement. The airplane’s maximum speed at sea level is 90 m/s. If the density of air at sea level is 1.225 kg/m³, the maximum pressure difference between the inlet and the throat of the venturimeter is __________ kPa (rounded off to two decimal places).
In a fluid flow, Mach number is an estimate of _________.
Consider a pair of point vortices with clockwise circulation \( \Gamma \) each. The distance between their centers is \( a \), as shown in the figure. Assume two-dimensional, incompressible, inviscid flow. Which one of the following options is correct?