Three particles of identical mass m are acted on only by their mutual gravitational attraction. they are located at the vertices of an equilateral triangle with sides of length d. consider the motion of any one of the particles about the system center of mass and use newton’s second law to determine the angular velocity ω required for d to remain constant.

Explanation:

The particles will be in constant angular motion . Let us consider forces on a single particle . It will experience three forces .

1 ) Attraction by other two masses

2 ) centripetal force necessary for circular motion.

Resultant of two like attractive forces F acting at 60 degree

= 2R Cos 30

= √3R

Centripetal force

= mω²r

so

mω²r  = √3R

R = GMm/ d² ( R is force of attraction on a particular mass by other masses )

r is radius of circle in which three particles rotate about their centre of mass .

Its value will be equal to

r = d / √3

Putting these values above we have

mω²d/√3  = √3 x GMm/ d²

ω =

cell differentiation  is how generic embryonic  cells  become specialized  cells. this occurs  through a process called gene expression. gene expression is the specific combination of genes that are turned on or off (expressed or repressed), and this is what dictates how a  cell  functions.

explanation:

when a device is used in a circuit in which the voltage is 81 v, the current flowing through the device is 3 a. what is the resistance of the device?

a. 27 ω

b. 40.5 a

c. 243 ω

d. 243 a

the correct answer is a. 27