Which of the following statements are true? a) the induced emf in acircuit is equal to the negative of the magnetic flux through thecircuit. b) there can be a nonzeroinduced emf at an instant when the flux through the circuit isequal to zero. c) the self-inductance of asolenoid is proportional to the rate of change of the current inthe solenoid. d) the magnetic energydensity at some point in space is proportional to the square of themagnitude of the magnetic field at that point. e) the inductance of asolenoid is proportional to the current in it.

Suppose that a comet that was seen in 563 a. d. by chinese astronomers was spotted again in year 1951. assume the time between observations is the period of the comet and take its eccentricity as 0.986. what are (a) the semimajor axis of the comet's orbit and (b) its greatest distance from the sun?

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 790 n/m. it is initially at rest on an inclined plane that is at an angle of 28 degrees with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is k = 0.14. in the initial position, where the spring is compressed by a distance of a = 0.18 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. b) if the spring pushes the block up the incline, what distance, l, in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.

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 ⇒