Prove that the angular momentum
H_G ^ of a rigid body about its mass
center is given by :
H_x =I_x ^ ω_x −I_(xy) ^ ω_y −I_(xz) ^ ω_z
H_y =−I_(yx) ^ ω_x +I_y ^ ω_y −I_(yz) ^ ω_z
H_z =−I_(zx) ^ ω_x −I_(zy) ^ ω_y +I_z ^ ω_z
where I_x ^ =∫(y^2 +z^2 )dm
I_(xy) ^ =∫xy dm ...and so on..
A and B play a game where each is
asked to select a number from 1 to 25.
If the two numbers match, both of them
win a prize. The probability that they
will not win a prize in a single trial is
a,b & c are distinct primes and
x,y,z∈{0,1,2,...}.
What is the number of divisors,
common to the numbers a^x b^y c^z ,
a^x b^z c^y ,a^y b^x c^z ,a^y b^z c^x ,a^z b^x c^y & a^z b^y c^z .
IF a_(1,) a_2 ,.....,a_(n−1) ,a_n are in AP then prove that
1/a_1 .a_n + 1/a_2 .a_(n−1) + 1/a_3 .a_(n−2) +...+1/a_n .a_1 =
2/a_1 +a_(n ) [1/a_(1 ) +1/a_2 +....+1/a_n ]