The schwarzschild metric external to a non-spinning spherical mass is -1 2m 2m 1- ds2 r2 (d0sin2 0dp2) dr2 dt2 1- where m is the mass of the body. (note that we are working in units where the speed of light c unity and the gravitational constant g are equal to (iii show from the metric that the proper time of a stationary clock far from the mass coincides with the coordinate t. show from the metric that the circumference of a great circle at radius r is just given by 27r (iv) a pulse of light is emitted radially by a by a stationary observer at radius r2. how long will it take the pulse to make the trip according to the observer at radius r2? you may assume that m/r < < 1. stationary light source at radius ri and detected (v) the observer at radius r2 uses a tape measure to directly measure the distance from ri to r2. using this result, what does this observer conclude was the average speed of the pulse

According to newtons universal law of gravitation, which would change the parh of the ball so it traces out widest curved path possible?

The magnetic field inside a superconducting solenoid is 4.50 t. the solenoid has an inner diameter of 6.20 cm and a length of 26.0 cm. determine (a) the magnetic energy density in the field and (b) the energy stored in the magnetic field within the solenoid.

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 ⇒