Find the mass and center of mass of the lamina that occupies the region D and has the given density function p. D is the triangular region with vertices (0, 0), (2, 1), (0, 3); p(x, y) = 2(x + y) m = 12 (x, y)

As seen in the image provided, a double-star system with stars of equal mass rotate in circular orbits around their mutual center of mass that is halfway between them. One of the stars (α) is bright. The other star (β) is its unseen dark companion. Our line of sight passes through the orbital plane such that once in every period, α approaches head-on, and once ever period it recedes directly away. The same is true for β. Suppose light always moves at speed c relative to the source that emits it (i.e., if v is the orbital speed of each star, light travels toward us at speed c + v from α when it is headed toward us, and at speed c - v when it is headed away from us, as depicted). The double-star system is a distance d away from Earth. How long would take light to get to Earth from α if the light is emitted when α is (i) coming toward us, and (ii) moving away from us?

Problem 7: The figure shows Superhero and Trusty Sidekick hanging motionless from a rope. Superhero's mass is 98 kg, while Trusty Sidekick's is 47 kg, and the mass of the rope is negligible. Randomized Variables m¡ = 98 kg m2 = 47 kg m 2 Part (a) Find the tension in the rope above Superhero in Newtons. Numeric : A numeric value is expected and not an expression. T = Part (b) Find the tension in the rope between Superhero and Trusty Sidekick in Newtons. Numeric : A numeric value is expected and not an expression. T' =

Consider a uniform solid hemisphere of radius r and mass m which is kept in contact with a smooth wall as shown in the figure. Find the normal reaction exerted on the sphere by the wall