Prove that
Question: $\frac{1}{x}-\frac{1}{y}+\frac{1}{z}=4 ; \frac{2}{x}+\frac{1}{y}-\frac{3}{z}=0$ $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=2 .(\mathrm{x}, \mathrm{y}, \mathrm{z} \neq 0)$ Solution: To find: $-x, y, z$ Given set of lines are : - $\therefore x=\frac{1}{2}, y=1, z=1$...
Read More →Consider the situation shown in figure (8-E2).
Question: Consider the situation shown in figure (8-E2). The system is released from rest and the block of mass $1.0 \mathrm{~kg}$ is found to have a speed $0.3 \mathrm{~m} / \mathrm{s}$ after it has descended through a distance of $1 \mathrm{~m}$. Find the coefficient of kinetic friction between the block and the table. Solution:...
Read More →The two blocks in an Atwood machine have masses
Question: The two blocks in an Atwood machine have masses $2.0 \mathrm{~kg}$ and $3.0 \mathrm{~kg}$. Find the work done by gravity during the fourth second after the system is released from rest. Solution:...
Read More →The heavier block in an Atwood machine has a mass twice
Question: The heavier block in an Atwood machine has a mass twice that of the lighter one. The tension in the string is $16.0 \mathrm{~N}$ when the system is set into motion. Find the decrease in the gravitational potential energy during the first second after the system is released from rest. Solution:...
Read More →Solve this following
Question: $\frac{2}{x}-\frac{3}{y}+\frac{3}{z}=10, \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=10$ $\frac{3}{x}-\frac{1}{y}+\frac{2}{z}=13$ Ans. $x=\frac{1}{2}, y=\frac{1}{3}, z=\frac{1}{5}$ Solution:...
Read More →A block of mass 30.0 kg is being brought down by a chain.
Question: A block of mass $30.0 \mathrm{~kg}$ is being brought down by a chain. If the block acquires a speed of $40.0 \mathrm{~cm} / \mathrm{s}$ in dropping down $2.00$ $\mathrm{m}$, find the work done by the chain during the process. Solution:...
Read More →A scooter company gives the following specifications about its product.
Question: A scooter company gives the following specifications about its product. Weight of the scooter $-95 \mathrm{~kg}$ Maximum speed $-60 \mathrm{~km} / \mathrm{h}$ Maximum engine power - $3.5 \mathrm{hp}$ Pick up time to get the maximum speed $-5 \mathrm{~s}$ Check the validity of these specifications. Solution:...
Read More →Solve this following
Question: If $\boldsymbol{A}=\left(\begin{array}{ccc}1 -2 0 \\ 2 1 3 \\ 0 -2 1\end{array}\right)$ and $B=\left(\begin{array}{ccc}7 2 -6 \\ -2 1 -3 \\ -4 2 5\end{array}\right)$, find $A B$ Hence, solve the system of equations: $x-2 y=10$ $2 x+y+3 z=8$ and $-2 y+z=7$ HINT: $A B=(11) /=A\left(\frac{1}{11} B\right)=I$ $A^{-1}=\left(\frac{1}{11}\right) B$ Solution:...
Read More →In a factory it is desired to lift 2000 kg
Question: In a factory it is desired to lift $2000 \mathrm{~kg}$ of metal through a distance of $12 \mathrm{~m}$ in 1 minute. Find the minimum horsepower of the engine to be used. Solution:...
Read More →An unruly demonstrator lifts a stone of mass
Question: An unruly demonstrator lifts a stone of mass $200 \mathrm{~g}$ from the ground and throws it at his opponent. At the time of projection, the stone is $150 \mathrm{~cm}$ above the ground and has a speed of $3.00 \mathrm{~m} / \mathrm{s}$. Calculate the work done by the demonstrator during the process. If it takes one second for the demonstrator to lift the stone and throw, what horsepower does he use? Solution:...
Read More →A water pump lifts water from a level
Question: A water pump lifts water from a level $10 \mathrm{~m}$ below the ground. Water is pumped at a rate of $30 \mathrm{~kg} / \mathrm{minute}$ with negligible velocity. Calculate the minimum horsepower the engine should have to do this. Solution:...
Read More →The US athlete Florence Griffith-Joyner won the
Question: The US athlete Florence Griffith-Joyner won the $100 \mathrm{~m}$ sprint gold medal at Seol Olympic 1988 setting a new Olympic record of $10.54 \mathrm{~s}$. Assume that she achieved her maximum speed in a very short-time and then ran the race with that speed till she crossed the line. Take her mass to be $50 \mathrm{~kg}$. (a) Calculate the kinetic energy of Griffith-Joyner at her full speed. (b) Assuming that the track, the wind etc. offered an average resistance of one tenth of her ...
Read More →The 200 m free style women's swimming gold medal
Question: The $200 \mathrm{~m}$ free style women's swimming gold medal at Seol Olympic 1988 went to Heike Friendrich of East Germany when she set a new Olympic record of 1 minute and $57.56$ seconds. Assume that she covered most of the distance with a uniform speed and had to exert $460 \mathrm{~W}$ to maintain her speed. Calculate the average force of resistance offered by the water during the swim. Solution:...
Read More →A projectile is fired from the top of a
Question: A projectile is fired from the top of a $40 \mathrm{~m}$ high cliff with an initial speed of $50 \mathrm{~m} / \mathrm{s}$ at an unknown angle. Find its speed when it hits the ground. Solution:...
Read More →A person is painting his house walls.
Question: A person is painting his house walls. He stands on a ladder with a bucket containing paint in one hand and a brush in other. Suddenly the bucket slips from his hand and falls down on the floor. If the bucket with the paint had a mass of $6.0 \mathrm{~kg}$ and was at a height of $2.0 \mathrm{~m}$ at the time it slipped, how much gravitational potential energy is lost together with the paint? Solution:...
Read More →Water falling from a 50 m high fall is to be used
Question: Water falling from a $50 \mathrm{~m}$ high fall is to be used for generating electric energy. If $1.8 \times 10^{5} \mathrm{~kg}$ of water falls per hour and half the gravitational potential energy can be converted into electric energy, how many $100 \mathrm{~W}$ lamps can be lit. Solution:...
Read More →A 250 g block slides on a rough horizontal table.
Question: A $250 \mathrm{~g}$ block slides on a rough horizontal table. Find the work done by the frictional force in bringing the block to rest if it is initially moving at a speed of $40 \mathrm{~cm} / \mathrm{s}$. If the friction coefficient between the table and the block is $0.1$, how far does the block move before coming to rest? Solution:...
Read More →A block of mass 2.0 kg is pushed down an inclined plane
Question: A block of mass $2.0 \mathrm{~kg}$ is pushed down an inclined plane of inclination $37^{\circ}$ with a force of $20 \mathrm{~N}$ acting parallel to the incline. It is found that the block moves on the incline with an acceleration of $10 \mathrm{~m} / \mathrm{s}^{2}$. If the block started from rest, find the work done (a) by the applied force in the first second, (b) by the weight of the block in the first second and (c) by the frictional force acting on the block in the first second. T...
Read More →A block of mass 2.0 kg kept at rest on an inclined plane
Question: A block of mass $2.0 \mathrm{~kg}$ kept at rest on an inclined plane of inclination $37^{\circ}$ is pulled up the plane by applying a constant force of $20 \mathrm{~N}$ parallel to the incline. The force acts for one second. (a) Show that the work done by the applied force does not exceed $40 \mathrm{~J}$. (b) Find the work done by the force of gravity in that one second if the work done by the applied force is $40 \mathrm{~J}$. (c) Find the kinetic energy of the block at the instant t...
Read More →A particle of mass $m$ moves on a straight line
Question: A particle of mass $m$ moves on a straight line with its velocity varying with the distance travelled according to the equation $v$ $=\mathrm{a} \sqrt{\mathrm{x}}$, where $\mathrm{a}$ is a constant. Find the total work done by all the forces during a displacement from $\mathrm{x}=0$ to $\mathrm{x}=\mathrm{d}$. Solution:...
Read More →Solve this following
Question: If $A=\left(\begin{array}{ccc}2 1 1 \\ 1 -2 -1 \\ 0 3 -5\end{array}\right)$, find $A^{-1}$ Using $A^{-1}$, solve the following system of linear equations: $2 x+y+z=1$ $x-2 y-z=\frac{3}{2}$ $3 y-5 z=9$ HINT: Here $A=\left(\begin{array}{ccc}2 1 1 \\ 1 -2 -1 \\ 0 3 -5\end{array}\right)$, $\mathbf{X}=\left(\begin{array}{l}x \\ y \\ z\end{array}\right)$ and $\mathbf{B}=\left(\begin{array}{l}1 \\ 3 / 2 \\ 9\end{array}\right)$ Solution:...
Read More →Find the average force needed to accelerate a car weighing
Question: Find the average force needed to accelerate a car weighing $500 \mathrm{~kg}$ from rest to $72 \mathrm{~km} / \mathrm{h}$ in a distance of $25 \mathrm{~m}$. Solution:...
Read More →Solve this following
Question: If $A=\left(\begin{array}{ccc}2 -3 5 \\ 3 2 -4 \\ 1 1 -2\end{array}\right)$, find $A^{-1}$ Using $A^{-1}$, solve the following system of equations: $2 x-3 y+5 z=11$ $3 x+2 y-4 z=-5$ $x+y-2 z=-3$ Solution: Given, $A=\left[\begin{array}{ccc}2 -3 5 \\ 3 2 -4 \\ 1 1 -2\end{array}\right]$...
Read More →Solve each of the following systems of equations using matrix method.
Question: Solve each of the following systems of equations using matrix method. $4 x+3 y+2 z=60$ $x+2 y+3 z=45$ $6 x+2 y+3 z=70$ Solution: To find: $-x, y, z$ Given set of lines are :-...
Read More →Solve each of the following systems of equations using matrix method.
Question: Solve each of the following systems of equations using matrix method. $x-y=3$ $2 x+3 y+4 z=17$ $y+2 z=7$ Solution:...
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