## Question

### Solution

Correct option is

The dimensions of the two sides of proportionality are

Equating the powers of dimensions on both sides, we have

#### SIMILAR QUESTIONS

Q1

The dimensions of angular momentum are

Q2

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?

Q3

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?

Q4

What is the SI unit of Plank’s constant?

Q5

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?

Q6

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?

Q7

What is the relationship between dyne and Newton of force?

Q8

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?

Q9

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

Q10

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