Units and Measu...

The dimensional formula of electric flux is:

If E, M, J and G denote energy, mass, angular momentum and gravitational constant respectively, then $$\frac{EJ^2}{M^5 G^2}$$ has the dimensions of 

Force F is given in terms of time t and distance x by $$F = A \sin Ct + B \cos Dx$$. Then the dimensions of $$\dfrac {A}{B}$$ and $$\dfrac{C}{D}$$ are:

The radius of the earth is $$6.37 \times 10^6 m$$ and its mass is $$5.975 \times 10^{24} kg$$. Find the earth's average density to appropriate significant figures.

In the relation $$y = r sin (\omega t - kx)$$, the dimensions of $$\omega/k$$ are

With due regard to significant figures, add the following:
a. 953 and 0.324
b. 953 and 0.625
c. 953.0 and 0.324
d. 953.0 and 0.374

A physical quantity $$x$$ depends on quantities $$y$$ and $$z$$ as follows: $$x = Ay + B \tan (C_z)$$, where $$A, B$$ and $$C$$ are constants. Which of the followings do not have the same dimensions?

If $$L$$ and $$R$$ denote inductance and resistance, respectively, then the dimensions of $$L/R$$ are

In the relation $$\dfrac{dy}{dt} = 2 \omega \sin (\omega t + \phi_0)$$, the dimensional formula for $$\omega t + \phi_0$$ is

The following observations were taken for determining the surface tension of water by capillary tube method : diameter of capillary , $$D = 1.25 \times 10^{-2} m$$. Taking $$ g = 9.80 m s^{-2}$$ and using the relation $$T = (rgh/2) \times 10^3 Nm^{-1}$$. what is the possible error in measurement of surface tension T?