It is known that density `rho` of air decreases with height y (in metres) as :
`rho = rho_(0) e^(-y//y_0)` where `rho_0 = 1.25 kg m^-3` is the density at sea level and `y_0` is a constant. This density variation is called the law of atmospheres. Obtain this law assuming the temperature of atomoshpere remains constant (isothermal conditions). Also assume that the value of g remains constant.

The density of air in atmoshpere decreases with height and can be expressed by the relaton rho = rho_0e^(-alphah where rho_0 is the density at sea level , alpha is a constant and h is the height, Calculate the atmospheric pressure at sea level. Assume g to be constatn. The numerical values of constants are : g = 9.8 ms^-2 , rho_0 = 1.3 kg m^-3 , alpha = 1.2 xx 10^-4 m^-1

The unit of length convenient on the nuclear scale is a fermi : 1 f = 10 ^-15 m . Nuclear sizes obey roughly the following empirical relation :- r=(r_0A)^(1/3) where ris the radius of the nucleus, Aits mass number, and r_o 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.

A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle |z-c|=a , the equation of a sphere of radius is |r-c|=a , where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at (-g, -f, -h) is x^2+y^2+z^2+2gx+2fy+2hz+c=0 and its radius is sqrt(f^2+g^2+h^2-c) . Q. The centre of the sphere (x-4)(x+4)+(y-3)(y+3)+z^2=0 is

A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle |z-c|=a , the equation of a sphere of radius is |r-c|=a , where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at (-g, -f, -h) is x^2+y^2+z^2+2gx+2fy+2hz+c=0 and its radius is sqrt(f^2+g^2+h^2-c) . Q. Radius of the sphere, with (2, -3, 4) and (-5, 6, -7) as xtremities of a diameter, is

A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m s^-1 to 3.5 m s^-1 in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force ?

A square of side L metres lies in the x-y plane in a region, where the magnetic field is given by B=B_0(2 hati + 3 hatj +4 hatk)T , where B_0 is constant. The maganitude of flux passing through the square is:

A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle |z-c|=a , the equation of a sphere of radius a is |r-c|=a , where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at (-g, -f, -h) is x^2+y^2+z^2+2gx+2fy+2hz+c=0 and its radius is sqrt(f^2+g^2+h^2-c) . Q. Equation of the sphere having centre at (3, 6, -4) and touching the plane rcdot(2hat(i)-2hat(j)-hat(k))=10 is (x-3)^2+(y-6)^2+(z+4)^2=k^2 , where k is equal to

The density of a non-uniform rod of length 1 m is given by rho (x) = a (1 + bx^2) where a and b are constant and 0 le x le 1 . The center of mass of the rod will be at

Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged if the density of ice is rho_1 = 0.971 g cm^-3 ?