Chapter Test: Unit & Measurement - 2 Free MCQs with solutions JEE

A unitless quantity -

The correct order in which the dimensions of

length increases in the following quantities is

(i) Volume,

(ii) Stress

(iii) Impulse

(iv) Planck's constant

If 1 g cm s^–1 = x newton-second, then the number x is equal to -

The velocity of a freely falling body changes as g^ph^q where g is acceleration due to gravity and h is the height. The values of p and q are

[ML²T^–3A^–2] is the dimensional formula of -

Consider a new system of units in which c (speed of light in vaccum), h (Planck's constant) and G (gravitational constant) are taken as fundamental units. Which of the following would represent mass in this new system ?

A wave is represented by y = a sin (At – Bx + C) where A, B, C are constants. The Dimensions of A, B, C are (here y and x are displacement and distance and t is time) -

Dimensional formula for the Planck's constant is -

Select the pair whose dimensions are same

The dimensions of angular momentum are -

Which of the following is unitless quantity ?

The dependency of speed of water surface waves (capillary waves) on the density of water (ρ) their wavelength (λ) and surface tension (γ) is -

The resistive force on a very-high-velocity object of area A passing through a gas of density ρ at a velocity v is

Force ~ A^r ρ^s v^t

Then –

If force, length and time were the fundamental units, then the dimensional formula of mass would have been -

To keep on object moving in a circle at constant speed requires a force F α m^av^br^c. According to dimensional analysis the a, b, c are -

A highly rigid cubical block A of small mass M and side L is fixed rigidly on the another cubical block of same dimensions and of low modulus of rigidity η such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on the horizontal surface. A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn, block A excutes small oscillations, the time period of which is given by –

If a and b are two physical quantities having different dimensions then which of the following can denote a new physical quantity

Choose the correct statement (S)

Planck's constant has the dimensions of :

The velocity 'v' (in cm/s) of a particle is given in terms of time 't' (in s) by the equation

v = at + 

The dimensions of a, b and c are

Force F is given in terms of time t and distance x by

F = A sin C t + B cos D x

Then the dimensions of  and  are given by