A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each.
Question: A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of 6.0 A in the wire. What value of current (with appropriate sense of circulation) in the windings of the sol...
Read More →Depict the galvanic cell in which the reaction Zn
Question: Depict the galvanic cell in which the reaction $\mathrm{Zn}(\mathrm{s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{s})$ takes place, further show: (i) which of the electrode is negatively charged, (ii) the carriers of the current in the cell, and (iii) individual reaction at each electrode. Solution: The galvanic cell corresponding to the given redox reaction can be represented as: $\mathrm{Zn}\left|\mathrm{Zn}_{\left(a_{q}\right)}^{2...
Read More →Solve the following system of inequalities graphically: 2x + y≥ 8, x + 2y ≥ 10
Question: Solve the following system of inequalities graphically:2x+y8,x+ 2y10 Solution: $2 x+y=8 \ldots(1)$ $x+2 y=10 \ldots(2)$ The graph of the lines, $2 x+y=8$ and $x+2 y=10$, are drawn in the figure below. Inequality (1) represents the region above the line, $2 x+y=8$, and inequality ( 2 ) represents the region above the line, $x+2 y=10$ Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the respective lines as f...
Read More →Solve the following system of inequalities graphically: x + y ≤ 6, x + y ≥ 4
Question: Solve the following system of inequalities graphically:x+y6,x+y4 Solution: $x+y \leq 6$ $x+y \geq 4$ The graph of the lines, $x+y=6$ and $x+y=4$, are drawn in the figure below. Inequality (1) represents the region below the line, $x+y=6$ (including the line $x+y=6$ ), and inequality (2) represents the region above the line, $x+y=4$ (including the line $x$ $+y=4$ ). Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the po...
Read More →Use Euclid's division algorithm to find the HCF of
Question: Use Euclid's division algorithm to find the HCF of (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 (iv) 184, 230 and 276 (v) 136, 170 and 255 (vi) 1260 and 7344 (vii) 2048 and 960 Solution: (i) Given integers are 225 and 135. Clearly 225 135. So we will apply Euclids division lemma to 225 and 135, we get, $867=(225)(3)+192$ Since the remainder $90 \neq 0 .$ So we apply the division lemma to the divisor 135 and remainder $90 .$ We get, $135=(90)(1)+45$ Now we apply the division lem...
Read More →A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil.
Question: A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil. If the current in the coil is 5.0 A, what is the (a)total torque on the coil, (b)total force on the coil, (c)average force on each electron in the coil due to the magnetic field? (The coil is made of copper wire of cross-sectional area 105m2, and the free electron density in copper is given to be about 1029m3.) Solution: Number of turns on the circular coil,n= 2...
Read More →Solve the following system of inequalities graphically: 2x – y > 1, x – 2y < –1
Question: Solve the following system of inequalities graphically:2xy 1,x 2y 1 Solution: $2 x-y1 \ldots(1)$ $x-2 y-1 \ldots(2)$ The graph of the lines, $2 x-y=1$ and $x-2 y=-1$, are drawn in the figure below. Inequality (1) represents the region below the line, $2 x-y=1$ (excluding the line $2 x-y=1$ ), and inequality (2) represents the region above the line, $x-2 y=-1$ (excluding the line $x-2 y=-1$ ). Hence, the solution of the given system of linear inequalities is represented by the common sh...
Read More →Compute the indicated products
Question: Compute the indicated products (i) $\left[\begin{array}{rr}a b \\ -b a\end{array}\right]\left[\begin{array}{rr}a -b \\ b a\end{array}\right]$ (ii) $\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]\left[\begin{array}{lll}2 3 4\end{array}\right]$ (iii)$\left[\begin{array}{rr}1 -2 \\ 2 3\end{array}\right]\left[\begin{array}{lll}1 2 3 \\ 2 3 1\end{array}\right]$ (iv) $\left[\begin{array}{lll}2 3 4 \\ 3 4 5 \\ 4 5 6\end{array}\right]\left[\begin{array}{ccc}1 -3 5 \\ 0 2 4 \\ 3 0 5\end{ar...
Read More →Solve the following system of inequalities graphically: x + y≥ 4, 2x – y > 0
Question: Solve the following system of inequalities graphically:x+y4, 2xy 0 Solution: $x+y \geq 4 \ldots(1)$ $2 x-y0 \ldots(2)$ The graph of the lines, $x+y=4$ and $2 x-y=0$, are drawn in the figure below. Inequality (1) represents the region above the line, $x+y=4$ (including the line $x+y=4$ ). It is observed that $(1,0)$ satisfies the inequality, $2 x-y0$. [2(1) $-0=20$ ] Therefore, inequality (2) represents the half plane corresponding to the line, $2 x-y=0$, containing the point $(1,0)$ [e...
Read More →Given the standard electrode potentials,
Question: Given the standard electrode potentials, $\mathrm{K}^{+} / \mathrm{K}=-2.93 \mathrm{~V}, \mathrm{Ag}^{+} / \mathrm{Ag}=0.80 \mathrm{~V}$ $\mathrm{Hg}^{2+} / \mathrm{Hg}=0.79 \mathrm{~V}$ $\mathrm{Mg}^{2+} / \mathrm{Mg}=-2.37 \mathrm{~V} . \mathrm{Cr}^{3+} / \mathrm{Cr}=-0.74 \mathrm{~V}$ Arrange these metals in their increasing order of reducing power. Solution: The lower the electrode potential, the stronger is the reducing agent. Therefore, the increasing order of the reducing power ...
Read More →A uniform magnetic field of 3000 G is established along the positive z-direction.
Question: A uniform magnetic field of 3000 G is established along the positivez-direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A. What is the torque on the loop in the different cases shown in Fig. 4.28? What is the force on each case? Which case corresponds to stable equilibrium? Solution: Magnetic field strength,B= 3000 G = 3000 104T = 0.3 T Length of the rectangular loop,l= 10 cm Width of the rectangular loop,b= 5 cm Area of the loop, A=lb= 10 5 = 50 cm2= 50 104...
Read More →Solve the following system of inequalities graphically: 2x + y≥ 6, 3x + 4y ≤ 12
Question: Solve the following system of inequalities graphically:2x+y6, 3x+ 4y12 Solution: 2x+y6 (1) 3x+ 4y12 (2) The graph of the lines, 2x+y= 6 and 3x+ 4y= 12, are drawn in the figure below. Inequality (1) represents the region above the line, 2x+y= 6 (including the line 2x+y= 6), and inequality (2) represents the region below the line, 3x+ 4y=12 (including the line 3x+ 4y=12). Hence, the solution of the given system of linear inequalities is represented by the common shaded region including t...
Read More →Arrange the following metals in the order in which they displace each other from the solution of their salts.
Question: Arrange the following metals in the order in which they displace each other from the solution of their salts. $\mathrm{Al}, \mathrm{Cu}, \mathrm{Fe}, \mathrm{Mg}$ and $\mathrm{Zn}$. Solution: A metal of stronger reducing power displaces another metal of weaker reducing power from its solution of salt. The order of the increasing reducing power of the given metals is $\mathrm{Cu}\mathrm{Fe}\mathrm{Zn}\mathrm{Al}\mathrm{Mg}$. Hence, we can say that Mg can displace Al from its salt soluti...
Read More →Solve the following system of inequalities graphically: 3x + 2y ≤ 12, x ≥ 1, y ≥ 2
Question: Solve the following system of inequalities graphically:3x+ 2y12,x1,y2 Solution: 3x+ 2y12 (1) x1 (2) y2 (3) The graphs of the lines, 3x+ 2y= 12,x= 1, andy= 2, are drawn in the figure below. Inequality (1) represents the region below the line, 3x+ 2y= 12 (including the line 3x+ 2y= 12). Inequality (2) represents the region on the right side of the line,x= 1 (including the linex= 1). Inequality (3) represents the region above the line,y= 2 (including the liney= 2). Hence, the solution of ...
Read More →Solve the following system of inequalities graphically: x ≥ 3, y ≥ 2
Question: Solve the following system of inequalities graphically:x3,y2 Solution: x3 (1) y2 (2) The graph of the lines,x= 3 andy= 2, are drawn in the figure below. Inequality (1) represents the region on the right hand side of the line,x= 3 (including the linex= 3), and inequality (2) represents the region above the line,y= 2 (including the liney= 2). Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the respective li...
Read More →Predict the products of electrolysis in each of the following:
Question: Predict the products of electrolysis in each of the following: (i) An aqueous solution of $\mathrm{AgNO}_{3}$ with silver electrodes (ii) An aqueous solution $\mathrm{AgNO}_{3}$ with platinum electrodes (iii) A dilute solution of $\mathrm{H}_{2} \mathrm{SO}_{4}$ with platinum electrodes (iv) An aqueous solution of $\mathrm{CuCl}_{2}$ with platinum electrodes. Solution: (i) $\mathrm{AgNO}_{3}$ ionizes in aqueous solutions to form $\mathrm{Ag}^{+}$and $\mathrm{NO}_{3}^{-}$ions. On electr...
Read More →A uniform magnetic field of 1.5 T exists in a cylindrical region of radius10.0 cm,
Question: A uniform magnetic field of 1.5 T exists in a cylindrical region of radius10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if, (a)the wire intersects the axis, (b)the wire is turned from N-S to northeast-northwest direction, (c)the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm? Solution: Mag...
Read More →Solve the given inequality graphically in two-dimensional plane: x > –3
Question: Solve the given inequality graphically in two-dimensional plane:x 3 Solution: The graphical representation ofx= 3 is given as dotted line in the figure below. This line divides thexy-plane in two half planes. Select a point (not on theline), which lies in one of the half planes, to determine whether the point satisfies the given inequality or not. We select the point as (0, 0). It is observed that, 0 3, which is true Also, it is evident that any point on the line does not satisfy the g...
Read More →Compute the following:
Question: Compute the following: (i) $\left[\begin{array}{rr}a b \\ -b a\end{array}\right]+\left[\begin{array}{ll}a b \\ b a\end{array}\right]$ (ii) $\left[\begin{array}{ll}a^{2}+b^{2} b^{2}+c^{2} \\ a^{2}+c^{2} a^{2}+b^{2}\end{array}\right]+\left[\begin{array}{cc}2 a b 2 b c \\ -2 a c -2 a b\end{array}\right]$ (iii) $\left[\begin{array}{lll}-1 4 -6 \\ 8 5 16 \\ 2 8 5\end{array}\right]+\left[\begin{array}{lll}12 7 6 \\ 8 0 5 \\ 3 2 4\end{array}\right]$ (v) $\left[\begin{array}{cc}\cos ^{2} x \si...
Read More →Solve the given inequality graphically in two-dimensional plane: y < –2
Question: Solve the given inequality graphically in two-dimensional plane:y 2 Solution: The graphical representation ofy= 2 is given as dotted line in the figure below. This line divides thexy-plane in two half planes. Select a point (not on theline), which lies in one of the half planes, to determine whether the point satisfies the given inequality or not. We select the point as (0, 0). It is observed that, 0 2, which is false Also, it is evident that any point on the line does not satisfy the ...
Read More →Solve the given inequality graphically in two-dimensional plane: 3y – 5x < 30
Question: Solve the given inequality graphically in two-dimensional plane:3y 5x 30 Solution: The graphical representation of 3y 5x= 30 is given as dotted line in the figure below. This line divides thexy-plane in two half planes. Select a point (not on theline), which lies in one of the half planes, to determine whether the point satisfies the given inequality or not. We select the point as (0, 0). It is observed that, 3(0) 5(0) 30 or 0 30, which is true Therefore, the upper half plane is not th...
Read More →The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time).
Question: The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? Is the force attractive or repulsive? Solution: Current in both wires,I= 300 A Distance between the wires,r= 1.5 cm = 0.015 m Length of the two wires,l= 70 cm = 0.7 m Force between the two wires is given by the relation, $F=\frac{\mu_{0} I^{2}}{2 \pi r}$ Where, $\mu_{0}=$ Perm...
Read More →Solve the given inequality graphically in two-dimensional plane: –3x + 2y ≥ –6
Question: Solve the given inequality graphically in two-dimensional plane: 3x+ 2y6 Solution: The graphical representation of 3x+ 2y= 6 is given in the figure below. This line divides thexy-plane in two half planes. Select a point (not on theline), which lies in one of the half planes, to determine whether the point satisfies the given inequality or not. We select the point as (0, 0). It is observed that, 3(0) + 2(0) 6 or 06, which is true Therefore, the lower half plane is not the solution regio...
Read More →A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends
Question: A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires. (a)What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero? (b)What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before? (Ignore the mass of the wires.) g = 9.8 m s2. Solution: Length of the rod...
Read More →Using the standard electrode potentials given in the Table 8.1,
Question: Using the standard electrode potentials given in the Table 8.1, predict if the reaction between the following is feasible: (a) $\mathrm{Fe}^{3+}(\mathrm{aq})$ and $\mathrm{I}^{-}(\mathrm{aq})$ (b) $\mathrm{Ag}^{+}(\mathrm{aq})$ and $\mathrm{Cu}(\mathrm{s})$ (c) $\mathrm{Fe}^{3+}$ (aq) and $\mathrm{Cu}$ (s) (d) $\mathrm{Ag}(\mathrm{s})$ and $\mathrm{Fe}^{3+}(\mathrm{aq})$ (e) $\mathrm{Br}_{2}$ (aq) and $\mathrm{Fe}^{2+}$ (aq) Solution: (a) The possible reaction between $\mathrm{Fe}_{(a ...
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