Obtain an expression for their relative speed of approach at any instant as a function of their separation distance d if the only interaction is their gravitational attraction to each other. Express your answer in terms of some or all of the variables m, d, and gravitational constant G. g

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

This is one type of line graph in which the independent variable is time plotted on the x axis and the dependent variable, also numerical, is plotted on the y axis.

Avertical clean glass piezometer tube has an inside diameter of d = 1 mm and is used to measure pressure in a horizontal pipe carrying water as shown. due to pressure in the pipe, the water at 20c rises into the tube to a height h. if the water pressure in the pipe is p = 500 pa gauge, estimate the height h: (a) without considering surface tension (b) with surface tension (capillary) effects. the contact angle  can be assumed at 30 deg