Question

Which of the following is having same dimensional formula? a) Work and power b) Radius of gyration and displacement c) Impulse and force d) Frequency and wavelength

Answer 1

Answer:

Work and torque both are represented as force multiplied by distance therefore must have the same dimensional formula.

Angular momentum can be written as L=mvr which gives its dimensions i.e. kg m

2

s

−1

and it is same as that of plank's constant.

As we know E=hν

∴ h=E/ν

However tension which is defined as force and surface tension which is defined as force per unit length must have different dimensional formulas.

Impulse is change is linear momentum over a time interval, therefore has the same dimension as the linear momentum.

Answer 2

Answer:

(a) Dimension of work = [M^1 L^2 T^-2]

Dimension of Force =[M^1 L^1 T^-2]

These both does not have same dimensions

(b) dimension of radius of gyration = [L]

Dimension of displacement = [L]

These both have same dimensions

(c) Dimension of impulse = [M^1 L^1 T^-1]

Dimension of force = [M^1 L^1 T^-2]

These both do not have same dimension

(d) dimension of frequency = [T^-1]

Dimension of wavelength = [L]

These both do not have same dimension

CORRECT ANSWER IS OPTION (B)

Hope this is helpful to you