3 57. 2068 Old Q. No. 56 A brass rod of length 0.40 m and steel rod of length 0.60 m, both are initially at 0°C are heated to 75°C. If the increase in lengths is the same for both the rods, calculate the linear expansivity of brass. The linear expansivity of steel is 12x10-6 °C-1. [4]

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 ⇒

Alarge box of mass m is pulled across a horizontal frictionless surface by a horizontal rope with tension t. a small box of mass m sits on top of the large box. the coefficients of static and

Suppose you plot the distance traveled by an object at various times and you discover that the graph is not a straight line. what does this indicate about the object's acceleration?