Unit & Dimension Test MCQ (With Solution) Level - 1 : Test 2 - Class 11 MCQ

The position x of a particle at time t is given by  where V₀ is constant and a > 0. The dimensions of V₀ and a are

The time dependence of a physical quantity P is given by , where α is a constant and t is time.Then constant α is

The frequency f of vibrations of mass m suspended from a spring of spring constant k is given by f = Cm^xk^y, where C is a dimensionless constant. The values of x and y are, respectively,

Write the dimensions of a/b in the relation , where P is the pressure, x is the distance, and t is the time.

Write the dimensions of a×b in the relation  , where E is the energy, x is the displacement, and t is time.

In the relation , where the letters have their usual meanings, the dimensions of V are 

Dimensional analysis cannot be used for :

The dimensions of   = permittivity of free space and E = electric field) are :

The vander Waals' equation for a gas is : 
Where P,V,R,T and n represent the pressure, volume, universal gas constant, absolute temperature and the number of moles of a gas, respectively, 'a' and 'b' are the constants. The ratio b/a will have the following

A gas bubble from an explosion under water oscillates with a period proportional to P^ad^bE^c where P is the static pressure, d is the density of water and E is the energy of explosion. Then a,b and c are :

The quantity X is given by  is the permitivity of free space, L is a length, ΔV is a potential difference and Δt is a time interval. The dimensional formula for X is same as that of :

Dimensions of  , where symbols have their usual meanings, are :

Which one of the following represents the correct dimensions of the coefficient of viscosity?

Planck's constant has the dimenstions of :

Dimensions of impulse are same as that of :

The dimensions of velocity gradient are :

The dimensional formula for surface tension is :