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Force: Equilibrium

Q- (a) Draw the free-body diagram of the link at B.

(b) If the spring has a stiffness of k=800 N/m and an unstretched length of 100 mm, determine the tension in cables BC and BD when the spring is held in the position shown.

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Thermodynamics

Q- A well-insulated rigid cylinder is divided into 2 compartments by a fixed conducting piston. Initially one side of the piston contains 1 m3 of O2 at 5 bar, 800C and the other side contains 1m3 of N2 at 7 bar, 200C.   Determine the final equilibrium temperature and pressure(s).

Solution: 

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Rotational Motion

Q- A solid wheel of mass 30 kg is rolled toward the left along a horizontal surface under the action of a horizontal force of magnitude 200 N, acting at the center of the wheel . If the friction is sufficient to prevent slipping, what is the magnitude of linear acceleration of the center of the whee…

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Current Electricity: Kirchhoff's Law

Q- Using mesh analysis, determine the current through R= 5Ω resistance and the potential Va.

Solution:

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Stationary Waves: Closed Organ Pipe

Q- An organ pipe is closed at one end and is 1.00 m long. Find the wavelength and frequency of the three lowest resonances which this pipe can produce. (speed of sound in air is 340 m/s)

Solution:

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Collision

Q- A truck with mass 5000 kg is heading east at 20 m/s. Meanwhile a car with mass 2500 kg is heading north at 30 m/s. The two vehicles collide at an intersection, get stuck together and the wreckage keeps moving to some direction.

(a) Is the collision elastic or inelastic?

(b) Find the speed of th…

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Modern Physics: Hydrogen Atom

Q- An electron orbiting a hydrogen atom has an initial energy of -0.544 eV. The atom emits a photon, then absorbs a photon, ending up with an energy of -3.4 eV. What was the wavelength of the emitted photon?

Solution:

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Thermodynamics

Q- A well-insulated rigid cylinder is divided in to 2 compartments by a conducting piston that is free to move freely. Initially one side of the piston contains 1 m3 of O2 at 5 bar, 800C and the other side contains 1m3 of N2 at 7 bar, 200C.   The piston is released and the system is allowed to come …

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Electrostatics: Coulomb's Law

Q- Two equally charged point mass of mass m each are suspended from a point by massless threads of length L. In equilibrium position each thread makes and angle ɵ with vertical.

(a) Find the ratio of magnitudes of horizontal electric force and vertical gravitational force on a the masses.

(b) Wh…

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Rotation: Sphere over Sphere

Q- A solid sphere of radius R starts at rest on top of a semicircular track of radius S., as shown in the figure. The sphere rolls without slipping along the track until it falls off the track at point B. Point A is a vertical distance H above the ground; the height of point B is unknown. You may as…

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Current Electricity: DC Circuits


Q- For the network of Figure,

(a) determine the value of R for maximum power to R.

(b) Determine the maximum power to R.

Solution:

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Quantum Physics: Potential Well

Q- An electron is trapped in an infinite well of width 11 nm. If the electron drops down 5 energy levels and, in the process, emits a photon with wavelength 642.94 nm, then what is the final energy of the electron?

Solution:

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Simple Harmonic Motion

(On request-Raunak)

Q- Two particles executes SHM of same amplitude of 20 cm with same period along the same line and about same equilibrium position. If the maximum distance between them is 20 cm, find their phase difference.

Solution:

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Projectile Motion

Q- A shall is fired from a hill of height ‘h’ at an angle of 450.  What is the magnitude of its velocity of projection as a function of its horizontal distance covered on ground x, acceleration due to gravity g and height h?

Solution:

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AC Circuits

Q- In an AC circuit the voltage across a resistive component is given by V(t) = 10 + 5 sin (3t). Find

(a) The voltage amplitude

(b) Root mean square voltage across the component Vrms.

Solution:

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Thermodynamics: Refrigerator

Q- A household refrigerator that has a power input of 450W and a COP of 2.5 is to cool 5 large watermelons, 10 kg each, to 10oC. If the melons are initially at 20oC, determine how long it will take for the refrigerator to cool them. The specific heat of melons = 4.2 kJ/(kg.oC)

Solution:

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Work Done by Variable Force

Q- The force verses displacement graph for a variable force acting on a particle during some displacement is given bellow (the thick lines)

(a) Calculate the total work done by this force on the particle.

(b) Which well-known physical device could produce the type of force during the first 10 seco…

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Heat and Thermodynamics

Q- A piston-cylinder device contains N2 gas, initially at 1.5 bar, 200C, 0.05 m3. The gas is now compressed in a polytropic process, PVn = constant, to 4 bar, 1500C. Determine the polytropic exponent ‘n’, the work done on the gas and the heat transfer.

Solution:

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Standing Waves

Q- One of the 63.5 cm long strings of an ordinary guitar is tuned to produce the not B (frequency 245 Hz) when vibrating in its fundamental mode.

(a) find the speed of the transverse wave on this string.

(b) If the tension in the string is doubled, what will be the new fundamental frequency of the…

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Electrostatics: Flux

Q. A point charge Q is on the axis of a short cylinder at its center. The diameter of the cylinder is equal to its length L (Fig.). What is the total flux through the curved sides of the cylinder?

Solution: 

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