## Question

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*, *T*is the surface tension of the liquid, θ the angle of contact and *g* the acceleration due to gravity?

### Solution

Since cos θ is dimensionless, using the dimensions of *T*, *r*, 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

#### SIMILAR QUESTIONS

The dimensions of angular momentum are

The gravitational force *F* between two masses *m*_{1} and *m*_{2} 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 *t*seconds is related to the cross-sectional area A of the tube and velocity *u*of 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 at*x* at time *t* is given by

Where *a*, *b* 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 *a*, *b* 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