From the relation `R = R_0A^(1//3)`, where `R_0` is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

The unit of length conventent on the nuclear scale is a fermi : 1f = 10^(-15) m. Nuclear sized obey roughly the following empirical relation: r = r_(0)A^(1//3) Where r is the radius of the nucleus, A its mass number, and r_(0) is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise . 2.27.

Differentiate a^(x) w.r.t x, where a is a positive constant

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density rho =A/r , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant is :

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), have volume charge density rho=A/r , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:

In terms of Rydberg constant R, the wave number of the first Balmer line is

A solid non conducting sphere of radius R has a non-uniform charge distribution of volume charge density, rho=rho_(0)r/R , where rho_(0) is a constant and r is the distance from the centre of the sphere. Show that : (i) the total charge on the sphere is Q=pirho_(0)R^(3) (ii) the electric field inside the sphere has a magnitude given by, E=(KQr^(2))/R^(4)

The resistance R = V//i , where V = 100 +- 5 V and I = 10+- 0.2 A . What is the total error in R ?

A solid sphere of radius R has a charge Q distributed in its volume with a charge density rho=kr^a , where k and a are constants and r is the distance from its centre. If the electric field at r=(R)/(2) is 1/8 times that r=R , find the value of a.