It is given that M = 185 kg and R = 1.65 m. What if an inner solid cylinder is cut out from it, with a radius of (1/2)R?

a) What is the moment of inertia around the central axis (as in the example) of this inner cylinder?

b) What is the moment of inertia of the remaining hollow cylinder around the same axis? (Notice that all answers are independent of the length L.)

Two charges, +9 µC and +15 µC, are fixed 1 m apart, with the second one to the right. Find the magnitude and direction of the net force (in N) on a −8 nC charge when placed at the following locations.

(a)

halfway between the two

magnitude ______________ N

(b)

half a meter to the left of the +9 µC charge

magnitude __________ N

(c)

half a meter above the +15 µC charge in a direction perpendicular to the line joining the two fixed charges (Assume this line is the x-axis with the +x-direction toward the right. Indicate the direction of the force in degrees counterclockwise from the +x-axis.)

magnitude__________ N

direction____________ ° counterclockwise from the +x-axis

A -3.00 nC point charge is at the origin, and a second -5.50 nC point charge is on the x-axis at x = 0.800 m.

Q1: Find the net electric force that the two charges would exert on an electron placed at point on the x-axis at x = 0.200 m.

Q2: Find the net electric force that the two charges would exert on an electron placed at point on the x-axis at x = 1.20 m.

Q3: Find the net electric force that the two charges would exert on an electron placed at point on the x-axis at x = -0.200 m.

A 1.20 kg iron cube at 343 K is placed in contact with olive oil at 283 K in a thermally insulated container. The specific heat of iron and oil is 450 J/(kg.K) and 1970 J/(kg.K), respectively. Both matters reach thermal equilibrium at 301.8 K, and there is no phase change and no chemical process in this example. (a) Find the amount of heat transfer for (i) the iron cube, and (ii) the olive oil. (b) Find the total change in entropy of this entire iron-oil system. Does your result validate the 2nd Law of Thermodynamics?

A solid S occupies the region of space located outside the sphere x² + y² + z² = 8 and inside the sphere x² + y² + (z - 2)² = 4. The density of this solid is proportional to the distance from the origin.

• Determine the center of mass of S.
• Is the center of mass located inside the solid S ? Carefully justify your answer.

A thin-walled capillary tube (diameter=5mm, length=1m) carries steam at 100degreesC The capillary is covered by a later of insulation (thermal conductivity=0.10W/mK) and thickness delta. Assume that the heat transfer coefficient in the outside ir is 25W/m2K and its temp is 25degreesC. Compute and plot the steady state heat loss from the tube as a function of the thickness of insulation used for the range 0<delta<2cm

how to solve the curvilinear motion in rocket

Compute the relative probability of finding an electron at the bottom of the conduction band relative to the probability of finding an electron at the top of the valence band in a silicon crystal at a temperature of (a) 3 K and (b) 300 K. Use Fermi-Dirac statistics. Compare your answer with the one given by the Boltzmann equation.

Explain why gravitational lensing is not a great way to discover large numbers of extrasolar planets given our current resources and technology. Also explain how, if you were determined and had access to enormous funding resources, you could still use gravitational lensing to discover a significant number of extrasolar planets. Conditions: you cannot leave the Earth’s surface, take an unlimitted amount of time, or send anything out from Earth to achieve your goal.

A)

A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 4 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass id riven by an external force equal to f(t) = 20 cos 3t use g=32 ft/s^2 for the acceleration due to gravity)

B)

A mass of 1 slug, when attached to a spring stretches it 2 feet and then comes to rest in the equilibrium position starting at t=0 an external force equal to f(t)=6 sin 4t is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. use g=32 ft/s^2 for the acceleration due to gravity.

Suppose a sinusoidal wave on a string, having amplitude A and travelling in the −xˆ direction, is partially reflected at the point x = 0, so that the reflected wave is in phase with the incident wave at x = 0 but has amplitude kA, where 0 ≤ k ≤ 1 is the reflection coefficient. a) Show that each point on the string undergoes simple harmonic motion and determine how the amplitude of the simple harmonic motion varies with x b) Find the ratio of maximum to minimum amplitude, known as the standing wave ratio

I need rapport about Waves and (difine ,types, equation ,conditions )of the waves and explain what's the different between wave phase velocity and group velocity...use good handwritten ...report not less than 3 pages..

A tennis ball is it at ground level. The ball reaches its maximum height above the ground level 1 sec. after being hit. Then 0.9 seconds after reaching its maximum height, the ball barely clears the net that is 3 m from where the tennis ball was hit. Assume the ground is level. How high is the net?  How far beyond the net does the tennis ball strike the ground?

How would you know define one to one correspondence when talking with the parents?