Using rutherford's observation that the number of a - particles scattered at angle and falling on unit ,deduce an expression for the probability of scattering area of the screen varied as between angles p& ¢+ d¢

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 ⇒

Three charge are arranged as shown in the diagram. the magnitude of the net electrical force acting on the +6 uc charge, rounded to the tenths place, is .

Agroup of monkeys is trying to cross the river in a rowboat. the maximum buoyant force on the rowboat is 2,000 n. the weight of the rowboat is 1,000 n. each monkey has a weight of 150 n. how many monkeys can safely cross in the rowboat at one time? explain your reasoning, including any calculations you used to find the answer.