In the expression `P = E l^2 m^-5 G^-2`, E,m,l and G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity.

If E is energy ,G is gravitational constant,l is impulse and M is masss the dimensions of (GIM^2)/(E^2) are same as that of :

Factorise the following expressions : 20 l^2 m + 30 a l m

The magnetic moment vectors mu_s and mu_l ( associated with the intrinsic spin angular momentum S and orbital angular momentum 1, respectively, of an electron are predicted by quantum theory (and verified experimentally to a high accuracy) to be given by: mu_s= -(e//m) S , mu_l= -(e//2m)l Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result.

a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c respectively. Show that : a/x+c/y=2 .

The 5th, 8th and 11th terms of a G.P. are p, q and x, respectively. Show that q^2=ps .

Deduce an expression in terms of mass of the earth 'M' And universal gravitational constant 'G' and gravity 'g'.

In the relation F = GM m//d^2 , the quantity G

Show that angular momentum is due to transverse component and does not depend on the radial component i.e. L = rp_theta

If velocity of light c, Plank's constant h and gravitational ontant G are taken as fundamental quantities then express mass, length and time in terms of dimensions of these quantities.