Show that each one of the following systems of equations is inconsistent.
Question: Show that each one of the following systems of equations is inconsistent. $3 x-y-2 z=2$ $2 y-z=-1$ $3 x-5 y=3$ Solution:...
Read More →A car goes on a horizontal circular road of radius
Question: A car goes on a horizontal circular road of radius $\mathrm{R}$, the speed increasing at a constant rate $\mathrm{dv} / \mathrm{dt}=\mathrm{a}$. The friction $\mathrm{dt}$ coefficient between the road and the tyre is $\mu$. Find the speed at which the car will skid. Solution:...
Read More →Show that each one of the following systems of equations is inconsistent.
Question: Show that each one of the following systems of equations is inconsistent. $x+2 y+4 z=12$ $y+2 z=-1$ $3 x+2 y+4 z=4$ Solution: are inconsistent....
Read More →Show that each one of the following systems of equations is inconsistent.
Question: Show that each one of the following systems of equations is inconsistent. $2 x-y+3 z=1$ $3 x-2 y+5 z=-4$ $5 x-4 y+9 z=14$ Solution:...
Read More →Show that each one of the following systems of equations is inconsistent.
Question: Show that each one of the following systems of equations is inconsistent. $x+y-2 z=5$ $x-2 y+z=-2$ $-2 x+y+z=4$ Solution:...
Read More →A motorcycle has to move with a constant speed
Question: A motorcycle has to move with a constant speed on an overbridge which is in the form of a circular arc of radius $\mathrm{R}$ and has a total length L. Suppose the motorcycle starts from the highest point. (a) What can its maximum velocity be for which the contact with the road is not broken at the highest point? (b) If the motorcycle goes at speed $1 / 42$ times the maximum found in part (a), where will it lose the contact with the road? (c) What maximum uniform speed can it maintain ...
Read More →Show that each one of the following systems of equations is inconsistent.
Question: Show that each one of the following systems of equations is inconsistent. $6 x+4 y=5$ $9 x+6 y=8$ Solution: To prove: Set of given lines are inconsistent....
Read More →Show that each one of the following systems of equations is inconsistent.
Question: Show that each one of the following systems of equations is inconsistent. $4 x-2 y=3$ $6 x-3 y=5$ Solution:...
Read More →A turn of radius 20 m is banked for the vehicles going
Question: A turn of radius $20 \mathrm{~m}$ is banked for the vehicles going at a speed of $36 \mathrm{~km} / \mathrm{h}$. If the coefficient of static friction between the road and the tyre is $0.4$, what are the possible speeds of a vehicle so that it neither slips down nor skids up? Solution:...
Read More →Show that each one of the following systems of equations is inconsistent.
Question: Show that each one of the following systems of equations is inconsistent. $2 x+3 y=5$ $6 x+9 y=10$ Solution:...
Read More →Suppose the amplitude of a simple pendulum having
Question: Suppose the amplitude of a simple pendulum having a bob of mass $\mathrm{m}$ is $\theta_{0}$. Find the tension in the string when the bob is at its extreme position. Solution:...
Read More →Suppose the bob of the previous problem has a speed
Question: Suppose the bob of the previous problem has a speed of $1.4 \mathrm{~m} / \mathrm{s}$ when the string makes an angle of $0.20$ radian with the vertical. Find the tension at this instant. You can use $\cos \theta=1-\theta^{2} / 2$ and $\sin \theta=0$ for small $\theta$. Solution:...
Read More →The bob of a simple pendulum of length
Question: The bob of a simple pendulum of length $1 \mathrm{~m}$ has mass $100 \mathrm{~g}$ and a speed of $1.4 \mathrm{~m} / \mathrm{s}$ at the lowest point in its path. Find the tension in the string at this instant. Solution:...
Read More →A simple pendulum is suspended from the ceiling of
Question: A simple pendulum is suspended from the ceiling of a car taking a turn of radius $10 \mathrm{~m}$ at a speed of $36 \mathrm{~km} / \mathrm{h}$. Find the angle made by the string of the pendulum with the vertical if this angle does not change during the turn. Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$. Solution:...
Read More →A mosquito is sitting on an L.P. record disc rotating
Question: A mosquito is sitting on an L.P. record disc rotating on a turn table at 333 per minute. The distance 3 of the mosquito from the centre of the turn table is $10 \mathrm{~cm}$. Show that the friction coefficient between the record and the mosquito is greater than It $\pi^{2} / 81$. Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$. Solution:...
Read More →A ceiling fan has a diameter (of the circle through
Question: A ceiling fan has a diameter (of the circle through the outer edges of the three blades) of $120 \mathrm{~cm}$ and rpm 1500 at full speed. Consider a particle of mass $1 \mathrm{~g}$ sticking at the outer end of a blade. How much force does it experience when the fan runs at full speed? Who experts this force on the particle? How much force does the particle exert on the blade along its surface? Solution:...
Read More →A stone is fastened to one end of a string and
Question: A stone is fastened to one end of a string and is whirled in a vertical circle of radius R. Find the minimum speed the stone can have at the highest point of the circle. Solution:...
Read More →In the Bohr model of hydrogen atom,
Question: In the Bohr model of hydrogen atom, the electron is treated as a particle going in a circle with the centre at the proton. The proton itself is assumed to be fixed in an inertial frame. The centripetal force is provided by the Coulomb attraction. In the ground state, the electron goes round the proton in a circle of radius $5.3 \times 10^{-11} \mathrm{~m}$. Find the speed of the electron in the ground state. Mass of the electron $=9.1 \times 10^{-31} \mathrm{~kg}$ and charge of the ele...
Read More →A circular road of radius 50 m has the angle of banking equal
Question: A circular road of radius $50 \mathrm{~m}$ has the angle of banking equal to $30^{\circ}$. At what speed should a vehicle go on this road so that the friction is not used? Solution:...
Read More →If the road of the previous problem is horizontal (no banking),
Question: If the road of the previous problem is horizontal (no banking), what should be the minimum friction coefficient so that a scooter going at $18 \mathrm{~km} / \mathrm{hr}$. does not skid? Solution:...
Read More →A park has a radius of 10 m.
Question: A park has a radius of $10 \mathrm{~m}$. If a vehicle goes round it at an average speed of $18 \mathrm{~km} / \mathrm{hr}$, what should be the proper angle of banking? Solution:...
Read More →Show that each one of the following systems of equations is inconsistent.
Question: Show that each one of the following systems of equations is inconsistent. $x+2 y=9$ $2 x+4 y=7$ Solution:...
Read More →If the horizontal force needed for the turn in the previous
Question: If the horizontal force needed for the turn in the previous problem is to be supplied by the normal force by the road, what should be the proper angle of banking? Solution:...
Read More →A scooter weighing 150 kg together
Question: A scooter weighing $150 \mathrm{~kg}$ together with its rider moving at $36 \mathrm{~km} / \mathrm{hr}$ is to take a turn of radius $30 \mathrm{~m}$. What horizontal force on the scooter is needed to make the turn possible? Solution:...
Read More →A particle moves in a circle of radius
Question: A particle moves in a circle of radius $1.0 \mathrm{~cm}$ at a speed given by $\mathrm{v}=2.0 \mathrm{t}$ where $\mathrm{v}$ is in $\mathrm{cm} / \mathrm{s}$ and $t$ in seconds. (a) Find the radial acceleration of the particle at $t=1 \mathrm{~s}$. (b) Find the tangential acceleration at $t=1 \mathrm{~s}$. (c) Find the magnitude of the acceleration at $\mathrm{t}=1 \mathrm{~s}$. Solution:...
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