Solve each of the following systems of equations using matrix method.
Question: Solve each of the following systems of equations using matrix method. $x+y+z=6$ $x+2 z=7$ $3 x+y+z=12$ Solution:...
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. $x+y+z=1$ $x-2 y+3 z=2$ $5 x-3 y+z=3$ Solution:...
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. $2 x-3 y+5 z=11$ $3 x+2 y-4 z=-5$ $x+y-2 z=-3$ Solution:...
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. $x+y+z=4$ $2 x-y+z=-1$ $2 x+y-3 z=-9$ Solution:...
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. $2 x-3 y+5 z=16$ $3 x+2 y-4 z=-4$ $x+y-2 z=-3$ Solution:...
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. $x+2 y+z=7$ $x+3 z=11$ $2 x-3 y=1$ Solution:...
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. $3 x+4 y+7 z=4$ $2 x-y+3 z=-3$ $x+2 y-3 z=8$ Solution:...
Read More →A table with smooth horizontal surface is placed
Question: A table with smooth horizontal surface is placed in a cabin which moves in a circle of a large radius $R$ (figure 7-E5). A smooth pulley of small radius is fastened to the table. Two masses $\mathrm{m}$ and $2 \mathrm{~m}$ placed on the table are connected through a string going over the pulley. Initially the masses are held by a person with the strings along the outward radius and then the system is released from rest (with respect to the cabin). Find the magnitude of the initial acce...
Read More →A car moving at a speed of 36 km/hr is taking
Question: A car moving at a speed of $36 \mathrm{~km} / \mathrm{hr}$ is taking a turn on a circular road of radius $50 \mathrm{~m}$. A small wooden plate is kept on the seat with its plane perpendicular to the radius of the circular road (figure 7-E4). A small block of mass $100 \mathrm{~g}$ is kept on the seat which rests against the plate. The friction coefficient between the block and the plate is $1.1=0.58$. (a) Find the normal contact force exerted by the plate on the block. (b) The plate i...
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. $x-y+z=1$ $2 x+y-z=2$ $x-2 y-z=4$ Solution: To find: $-x, y, z$ Given set of lines are : -...
Read More →A table with smooth horizontal surface is fixed in a cabin
Question: A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity co in a circular path of radius $\mathrm{R}$ (figure 7-E3). A smooth groove $\mathrm{AB}$ of length $\mathrm{L}(\ll \mathrm{R}$ ) is made on the surface of the table. The groove makes an angle 0 with the radius $\mathrm{OA}$ of the circle in which the cabin rotates. A small particle is kept at the point A in the groove and is released to move along $A B$. Find the time taken by the p...
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. $2 x+8 y+5 z=5$ $x+y+z=-2$ $x+2 y-z=2$ Solution:...
Read More →A block of mass m moves on a horizontal circle against
Question: A block of mass $m$ moves on a horizontal circle against the wall of a cylindrical room of radius $R$. The floor of the room on which the block moves is smooth but the friction coefficient between the wall and the block is $g$. The block is given an initial speed $v_{0}$. As a function of the speed $v$ write (a) the normal force by the wall on the block, (b) the frictional force by the wall and (c) the tangential acceleration of the block. (d) Integrate the tangential acceleration $(d ...
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. $4 x-3 y=3$ $3 x-5 y=7$ Solution:...
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. $2 x-3 y+1=0$ $x+4 y+3=0$ Solution:...
Read More →What is the radius of curvature of the parabola traced out by the projectile
Question: What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle $0 / 2$ with the horizontal? Solution:...
Read More →A particle is projected with a speed
Question: A particle is projected with a speed $\mathrm{u}$ at an angle 0 with the horizontal. Consider a small part of its path near the highest position and take it approximately to be a circular arc. What is the radius of this circle? This radius is called the radius of curvature of the curve at the point. Solution:...
Read More →A hemispherical bowl of radius R is rotated about
Question: A hemispherical bowl of radius $R$ is rotated about its axis of symmetry which is kept vertical. A small block is kept in the bowl at a position where the radius makes an angle $\theta$ with the vertical. The block rotates with the bowl without any slipping. The friction coefficient between the block and the bowl surface is u. Find the range of the angular speed for which the block will not slip. Solution:...
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. $5 x+7 y+2=0$ $4 x+6 y+3=0$ Solution: To find: $-x, y$ 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. $x+2 y=1$ $3 x+y=4$ Solution:...
Read More →In a children's park a heavy rod is pivoted at the centre
Question: In a children's park a heavy rod is pivoted at the centre and is made to rotate about the pivot so that the rod always remains horizontal. Two kids hold the rod near the ends and thus rotate with the rod (figure 7-E2). Let the mass of each kid be $15 \mathrm{~kg}$, the distance between the points of the rod where the two kids hold it be $3.0 \mathrm{~m}$ and suppose that the rod rotates at the rate of 20 revolutions per minute. Find the force of friction exerted by the rod on one of th...
Read More →A track consists of two circular parts
Question: A track consists of two circular parts $\mathrm{ABC}$ and CDE of equal radius $100 \mathrm{~m}$ and joined smoothly as shown in figure (7-E1). Each part subtends a right angle at its centre. A cycle weighing $100 \mathrm{~kg}$ together with the rider travels at a constant speed of $18 \mathrm{~km} / \mathrm{h}$ on the track. (a) Find the normal contact force by the road on the cycle when it is at B and at D. (b) Find the force of friction exerted by the track on the tyres when the cycl...
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. $3 x+4 y-5=0$ $x-y+3=0$ Solution:...
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. $5 x+2 y=4$ $7 x+3 y=5$ Solution:...
Read More →A block of mass m is kept on a horizontal ruler.
Question: A block of mass $m$ is kept on a horizontal ruler. The friction coefficient between the ruler and the block is g. The ruler is fixed at one end and the block is at a distance $L$ from the fixed end. The ruler is rotated about the fixed end in the horizontal plane through the fixed end. (a) What can the maximum angular speed be for which the block does not slip? (b) If the angular speed of the ruler is uniformly increased from zero at an angular acceleration a, at what angular speed wil...
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