# ## Solution Search

• January 30, 2023
• September 11, 2021
• August 6, 2021
• Iriam
August 4, 2021
• Abhigyan Martin Ninama
September 8, 2017

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### Linear Motion Combined with Rotaional Motion

Q- A m1 = 16.0 kg object and a m2 = 12.5 kg object are suspended, joined by a cord that passes over a pulley with a radius of 10.0 cm and a mass of 3.00 kg. The cord has a negligible mass and does not slip on the pulley. The pulley rotates on its axis without friction. The objects start from rest 3.…

### EMI: Induced Current

Q-Two parallel circular loops of wire having the same common axis.  The smaller loop of radius r, and is above the larger loop (radius R) by a distance X>>R.  the magnetic field due to the counterclockwise current i in the larger loop is nearly uniform throughout the smaller loop.  Suppose that x is…

### Circular Motion

(Requested by Tricky Bits)

Q- A wheel 1.9 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.15 rad/s2. The wheel starts from rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3o with the hori…

### Conservation of Energy: Motion in Vertical Plane

Q- A pendulum consists of a string of length L and a bob of mass M.  The string is brought to a horizontal position and given the minimum initial speed enabling a pendulum to make a full turn in the vertical plane.

a) what is the maximum kinetic energy K of the bob?

b) what is the tension …

### Electrostatics: Capacitance

Q- Five 1 inch square plates are arranged as shown in figure. The plate spacings are 0.01 inch. The arrangement is to be used for a displacement transducer by observing the change in capacitance with the distance x. Calculate the sensitivity of the device in picofarads per inch. Assume that the plat…

### Differentiation

Q- At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute.  The diameter of the base of the cone is 3 times the altitude.  At what rate is the height of the pile changing when the pile is 15 feet high?

Solution:

### Magnetic Force

Q- A rectangular coil of wire, 22.0 cm by 35.0 cm and carrying a current 1.40 A, is oriented with the plane of its loop perpendicular to a uniform 1.50 T magnetic field in to the plane of the coil.

a) Calculate the net force and torque which the magnetic field exerts on the coil.

b) The coil is ro…

### Refraction Through A Prism

Q- A horizontal beam of light that is incident on an equilateral prism. The base of the prism is horizontal. The prism (n = 1.40) is surrounded by a liquid whose index of refraction is 1.60. Determine the angle of emergence from the other surface, that is the exiting light makes with the normal to t…

### Sound and Vibration

Q- A heavy piece of hanging sculpture is suspended by a 90 cm long, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequency of 80 Hz. What is the mass of the sculpture?

Solution:

### Mechanics: Conservation of momentum

Q- Two railroad cars moving on same track towards each other. One of mass 10000 kg with speed 0.3 m/s and the other of mass 15000 kg with speed of 0.1 m/s.

(a) What is the magnitude of their common velocity after they coule together?

(b) How much kinetic energy is lost during collision?

So…

### Thermodynamics: Specific Heat Capacity

Q- A well-sealed room contains 80 kg of air at 200 kPa and 25°C. Now solar energy enters the room from windows at an average rate of 1 kJ/s while a 100-W fan is turned on to circulate the air in the room. If heat transfer through the walls is negligible, what will be the air temperature in the room …

### Rotation: Toppling

Q- I have a 1.5 m tall air compressor that weights 50 kg with a 0.5 m square base. I have a cart that is 1m x 2m. The surface of the cart where the compressor will be mounted is 0.25 m off the ground. The cart wheels are in the corners, it is rated to carry 500 kg and weighs 75 kg. If the compressor…

### Electrostatics: Induced Charges

Q- A point charge q is placed between two infinitely large conducting parallel planes with distance d between them, such that it is at a distance x from one plane.  Find the charges induced on each plane.

Solution:

### Motion In A Plane

Q- A small ball is suspended from point A by a thread of length L.  A nail is driven into the wall at a distance of L/2 below A, at O.  The ball is drawn so that the thread takes up a horizontal position.

(a) At what point in the ball’s trajectory will the tension in the thread disappear?
(b)…

### Alternating Currents

Q - An AC generator supplies an rms voltage of 5.00 V to an RC circuit. At a frequency of 20.0 kHz the rms current in the circuit is 37.0 mA; at a frequency of 30.0 kHz the rms current is 50.0 mA. What are the values of R and C in this circuit?

Solution:

### kinematics

(Requested by Merjan)

Q – Two cars were moving on parallel lanes in one direction. One car had speed 60 km/hour, while the other had speed of 65 km/hr. At time 8:30 AM, the distance between the cars was 8 km.

(a)  How far a way from each another the were at 9:20 AM that day?

(b)  At what ti…

### Ray Optics: Refraction

Q- Red light (n = 1.520) and violet light (n = 1.538) traveling in air are incident on a slab of crown glass. Both colors emerge from the glass at the same angle of refraction. The red light has an angle of incidence of 35.96°. What is the angle of incidence of the violet light? Give your answer to …

### Speed of Bullet

Q- A bullet is shot through two cardboard disks attached a distance D apart to a shaft turning with a rotational period T, as shown. Derive a formula for the bullet speed v in terms of D, T and a measured angle θ between the position of the hole in the first disk and that of the hole in the second.…

### Errors: Measuring Speed of Light

Q- Galileo attempted to measure the speed of light by measuring the time elapsed between his opening a lantern and his seeing the return light from his assistant’s lantern, which is opened when the assistant sees the light from Galileo’s lantern. What distance d must separate Galileo from his assist…

### Harmonic Oscillations

Q- A harmonic force F0 sin(ωt) is applied to mass m1 which in turn is coupled to springs of spring constants k1, k2 and k3. Let x1 and x2 ­be the deviations from equilibrium for m1 and m2, respectively.  The blocks moves on a horizontal frictionless table.

(a) Write the equations of motion for …

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