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).

R = R_0A^(1//3) ( R_0 = constant, A = Mass Number), R = radius of nucleus. Taking the relation show that of nuclear density does not depend on mass number A .

The radius of nucleus: R=R_0A^(1/3) ( R_0 =constant, A=mass No.). Taking the relation, show that the nuclear density does not depend on mass number A.

For a nucleus which is nearly spherical in shape r=r_0 A^(1/3) , where r is the radius and A is the mass number and r_0 is a constant of value 1.2xx10^(-15) m. If the mass of the neutrons and protons are equal and equal to 1.67xx10^(-27) kg, prove that density of the nucleus is 2.3xx10^14 times the density of water.

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

If z=z_0+A( bar z -( bar z _0)), w h e r eA is a constant, then prove that locus of z is a straight line.

Show that the velocity of a body released at distance r from the centre of the earth, when it strikes the surface of the earth is given by , v=sqrt(2GM(1/R-1/r)) where R and M are the radius and mass of the earth. Also show that the velocity with which meteorites strike the earth's surface is equal to escape velocity.

E^(0)" for " M^(2+)(aq) + e to M(s) (where, M = Ca, Sr or Ba) is nearly constant. Comment.