If a number of little
droplets all of the same
radius r coalesce to
form a single
drop of radius R.show
that the rise in temperature
is given by
((3T)/(pJ))((1/r)−(1/R))
where T is surface tension
of water and J is mechanical
equivalent of heat
The points A, B, C represent the complex numbers z_1 , z_2 , z_3
respectively. And G is the centroid of the triangle A B C, if
4z_1 + z_2 + z_3 = 0, show that the origin is the mid point of AG.
Show that the locus of a
point which moves so
that its distance from
the point (ae,0) is e times
its distance from the
line x=(a/e) is given by the
equation
(x^2 /a^2 )+(y^2 /(a^2 (1−e^2 )))=1
Given that z_1 = R_1 + R + jωL ; z_2 = R_2 ; z_3 = (1/(jωC_3 ))
and z_4 = R_4 + (1/(jωC_4 )) and also that z_1 z_3 = z_2 z_4 , express
R and L in terms of the real constants R_1 , R_2 , R_4 , C_3 and C_4
Answer: R = ((R_2 C_3 − R_1 C_4 )/C_4 ) , L = R_2 R_4 C_3