Which One Of The Following Relations Is Dimensionally Consistent Where h is Height To Which A Liquid Of Density ρ Rises In A Capillary Tube Of Radius, r, Tis The Surface Tension Of The Liquid, θ The Angle Of Contact And g the Acceleration Due To Gravity?

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Which one of the following relations is dimensionally consistent where h is height to which a liquid of density ρ rises in a capillary tube of radius, rTis the surface tension of the liquid, θ the angle of contact and g the acceleration due to gravity?


Correct option is

Since cos θ is dimensionless, using the dimensions of Tr, ρ and g, it is easy to see that  is only one that is dimensionally consistent. The dimensions of h are the same as those of 



The dimensions of angular momentum are


The gravitational force F between two masses m1 and m2 separated by a distance r is given by  where G is the universal gravitational constant. What are the dimensions of G?



According to the quantum theory, the energy E of a photon of frequency v is given by 


Where h is Plank’s constant. What is the dimensional formula for h?


What is the SI unit of Plank’s constant?



The volume V of water passing any point of a uniform tube during tseconds is related to the cross-sectional area A of the tube and velocity uof water by the relation  


Which one of the following will be true?



The frequency n of vibrations of uniform string of length l and stretched with a force F is given by


Where p is the number of segments of the vibrating string and m is a constant of the string. What are the dimensions of m?


What is the relationship between dyne and Newton of force?



When a wave traverses a medium, the displacement of a particle located atx at time t is given by 


Where ab and c are constants of the wave. Which of the following are dimensionless quantities?



The Vander Waal equation for n moles of a real gas is 


Where P is the pressure, V is the volume, T is the absolute temperature, R is the molar gas constant and ab are Vander Waal constants. The dimensions of a are the same as those of


In velocity (V), acceleration (A) and force (F) are taken as fundamental quantities instead of mass (M), length (L) and time (T), the dimensions of Young’s modulus would be