Solve this following
Question: Prove that $f(x)=\left\{\begin{array}{l}2-x, \text { when } x2 \\ 2+x, \text { when } x \geq 2\end{array}\right.$ is discontinuous at $x=2$ Solution:...
Read More →A wave pulse is travelling on a string with a speed v towards
Question: A wave pulse is travelling on a string with a speed $v$ towards the positive $x$-axis. The shape of the string at $t=0$ is given by $\mathrm{g}(\mathrm{x})=\mathrm{A} \sin (\mathrm{x} / \mathrm{a})$, where $\mathrm{A}$ and a are constants. (a) What are the dimensions of A and a? (b) Write the equation of the wave for a general time $t$, if the wave of the speed is $t$. Solution:...
Read More →The displacement of the particle at x=0 of a stretched string carrying
Question: The displacement of the particle at $x=0$ of a stretched string carrying a wave in the positive $x$-direction is given by $\mathrm{f}(\mathrm{t})=\mathrm{A} \sin (\mathrm{t} / \mathrm{T})$ The wave speed is $v$. Write the wave equation. Solution:...
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Question: Prove that $f(x)=\left\{\begin{array}{c}\frac{1-\cos x}{x^{2}}, \text { when } x \neq 0 ; \\ 1, \text { when } x=0\end{array}\right.$ is discontinuous at $x=0$ Solution:...
Read More →A pulse travelling on a string is represented by the function
Question: A pulse travelling on a string is represented by the function $y=\frac{a^{3}}{(x-v t)^{2}+a^{2}}$ Where $a=5 \mathrm{~mm}$ and $\mathrm{v}=20 \mathrm{~cm} / \mathrm{s}$. Sketch the shape of the string at $\mathrm{t}=0,1 \mathrm{~s}, 2 \mathrm{~s}$. Take $x=0$ in the middle of the string. Solution:...
Read More →The Figure shows a wave pulse at t=0.
Question: The Figure shows a wave pulse at $t=0$. The pulse moves to the right with a speed at $10 \mathrm{~cm} / \mathrm{s}$. Sketch the shape of the string at $t=1 \mathrm{~s}, 2 \mathrm{~s}, 3 \mathrm{~s}$. Solution:...
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Question: Prove that $f(x)=\left\{\begin{array}{c}\frac{\sin 3 x}{x}, \text { when } x \neq 0 ; \\ 1, \text { when } x=0\end{array}\right.$ is discontinuous at $x=0$ Solution:...
Read More →The equation of a wave travelling on a string stretched along
Question: The equation of a wave travelling on a string stretched along the $X$-axis is given by $\mathrm{Y}=\mathrm{A} . e^{-\left(\frac{x}{a}+\frac{t)^{2}}{T}\right.}$ (a) Write the dimensions of $A$, a and $T$. (b) Find the wave speed (c) In which direction is the wave travelling (d) Where is the maximum of the pulse located at $t=T$ ? At $t=2 T$ ? Solution: at $t=T ; x=-a$ $t=2 T ; x=-2 a$...
Read More →A wave pulse passing on a string with a speed of 40 cm/s
Question: A wave pulse passing on a string with a speed of $40 \mathrm{~cm} / \mathrm{s}$ in the negative $x$-direction has its maximum at $x=0$ at $t=0$. Where will this maximum be located at $t=5 \mathrm{~s}$ ? Solution:...
Read More →Prove that
Question: Prove that $f(x)=\left\{\begin{aligned} \frac{x^{2}-25}{x-5}, \text { when } x \neq 5 \\ 10, \text { when } x=5 \end{aligned}\right.$ is continuous at $x=5$ Solution:...
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Question: Prove that $f(x)=\left\{\begin{aligned} \frac{x^{2}-x-6}{x-3}, \text { when } x \neq 3 \\ 5, \text { when } x=3 \end{aligned}\right.$ is continuous at $x=3$ Solution:...
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Question: Show that $f(x)=\left(x^{2}+3 x+4\right)$ is continuous at $x=1$. Solution:...
Read More →Solve this following
Question: Show that $f(x)=x^{2}$ is continues at $x=2$. Solution:...
Read More →Water flows at a speed of 6 cm/s through a tube of radius 1cm.
Question: Water flows at a speed of $6 \mathrm{~cm} / \mathrm{s}$ through a tube of radius $1 \mathrm{~cm}$. Coefficient of viscosity of water at room temperature is $0.01$ poise. Calculating the Reynolds number. Is it a steady flow? Solution:...
Read More →Estimate the speed of vertically falling raindrops from
Question: Estimate the speed of vertically falling raindrops from the following data. Radius of the drops $=0.02 \mathrm{~cm}$, viscosity of air $=$ $1.8 \times 10^{-4}$ poise, $g=9.9 \mathrm{~m} / \mathrm{s}^{2}$ and density of water $=1000 \mathrm{~kg} / \mathrm{m}^{3}$. Solution:...
Read More →A metal sphere of radius 1 mm and mass 50 mg
Question: A metal sphere of radius $1 \mathrm{~mm}$ and mass $50 \mathrm{mg}$ falls vertically in glycerine. Find (a) the viscous force exerted by the glycerine on the sphere when the speed of the sphere is $1 \mathrm{~cm} / \mathrm{s}$, (b) the hydrostatic force exerted by the glycerine on the sphere and (c) the terminal velocity with which the sphere will moved down without acceleration. Density of glycerine = $1260 \mathrm{~kg} / \mathrm{m}^{3}$ and its coefficient viscosity at room temperatu...
Read More →A wire forming a loop is dipped into soap solution and
Question: A wire forming a loop is dipped into soap solution and taken out so that a film of soap solution is formed. A loop of $6.28 \mathrm{~cm}$ long thread is gently put on the film and the film is pricked with a needle inside the loop. The thread loop takes the shape of a circle. Find the tension in the thread. Surface tension of soap solution $=0.030 \mathrm{~N} / \mathrm{m}$. Solution:...
Read More →Solve this following
Question: If $A=\left(\begin{array}{cc}1 -1 \\ 2 -1\end{array}\right)$ and $B=\left(\begin{array}{cc}a 1 \\ b -1\end{array}\right)$ and $(A+B)^{2}=\left(A^{2}+B^{2}\right)$ then A. $a=2, b=-3$ B. $a=-2, b=3$ C. $a=1, b=4$ D. none of these Solution:...
Read More →Consider an ice cube of edge
Question: Consider an ice cube of edge $1.0 \mathrm{~cm}$ kept in a gravity free hall. Find the surface area of the water when the ice melts. Neglect the difference in densities of ice and water. Solution:...
Read More →Two larger glass plates are placed vertically and
Question: Two larger glass plates are placed vertically and parallel to each other inside a tank of water with separation between the plates equal to $1 \mathrm{~mm}$. find the rise of water in the space between the plates. Surface tension of water $=0.075 \mathrm{~N} / \mathrm{m}$. Solution:...
Read More →Which one of the following is a scalar matrix?
Question: Which one of the following is a scalar matrix? A. $\left(\begin{array}{ll}1 1 \\ 1 1\end{array}\right)$ B. $\left(\begin{array}{ll}6 0 \\ 0 3\end{array}\right)$ c. $\left(\begin{array}{cc}-8 0 \\ 0 -8\end{array}\right)$ D. None of these Solution:...
Read More →The lower end of a capillary tube of radius 1 mm is dipped vertically into mercury.
Question: The lower end of a capillary tube of radius $1 \mathrm{~mm}$ is dipped vertically into mercury. (a) Find the depression of mercury column in the capillary. (b) If the length dipped inside is half the answer of part (a), find the angle made by the mercury surface at the end of the capillary with the vertical. Surface tension of mercury $=0.465 \mathrm{~N} / \mathrm{m}$ and the contact angle of mercury with glass $=135^{\circ}$. Solution:...
Read More →Solve this following
Question: If $\mathrm{A}$ is a 3-rowed square matrix and $|3 \mathrm{~A}|=\mathrm{k}|\mathrm{A}|$ then $\mathrm{k}=$ ? A. 3 B. 9 C. 27 D.1 Solution: Since the matrix is of order 3 so 3 will be taken common from each row or column. So, $k=27$ Tagging...
Read More →A capillary tube of radius 1 mm is kept vertical with the lower end in water.
Question: A capillary tube of radius $1 \mathrm{~mm}$ is kept vertical with the lower end in water. (a) Find the height of water raised in the capillary. (b) If the length of the capillary tube is half the answer of part (a), find the angle $\theta$ made by the water surface in the capillary with the wall. Solution:...
Read More →Solve this following
Question: If $A$ is a square matrix then $\left(A-A^{\prime}\right)$ is A. A null matrix B. An identity matrix C. A symmetric matrix D. A skew-symmetric matrix Solution:...
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