A drop of mercury of radius
Question: A drop of mercury of radius $2 \mathrm{~mm}$ is split into 8 identical droplets. Find the increase in surface energy. Surface tension of mercury $=0.465 \mathrm{~J} / \mathrm{m}^{2}$. Solution:...
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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:...
Read More →Find the surface energy of water kept in a cylindrical vessel
Question: Find the surface energy of water kept in a cylindrical vessel of radius $6.0 \mathrm{~cm}$. Surface tension of water $=0.075 \mathrm{~J} / \mathrm{m}^{2}$. Solution:...
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Question: If $A=\left(\begin{array}{ccc}3 4 1 \\ 1 0 -2 \\ -2 -1 2\end{array}\right)$ then $A^{-1}=?$ A. $\left(\begin{array}{ccc}2 9 -8 \\ -2 8 7 \\ -1 5 -4\end{array}\right)$ B. $\left(\begin{array}{ccc}-2 9 -8 \\ 2 8 7 \\ -1 -5 4\end{array}\right)$ c. $\left(\begin{array}{ccc}-2 -9 -8 \\ 2 8 7 \\ -1 -5 -4\end{array}\right)$ D. None of these Solution: $\left(\begin{array}{ccc}-2 -9 -8 \\ 2 8 7 \\ -1 -5 -4\end{array}\right)$...
Read More →A capillary tube of radius
Question: A capillary tube of radius $0.50 \mathrm{~mm}$ is dipped vertically in a pot of water. Find the difference between the pressure of the water in the tube $5.0 \mathrm{~cm}$ below the surface and the atmospheric pressure. Surface tension of water $=0.075 \mathrm{~N} / \mathrm{m}$. Solution:...
Read More →A barometer is constructed with its tube having radius
Question: A barometer is constructed with its tube having radius $1.0 \mathrm{~mm}$. Assume that the surface of mercury in the tube is spherical in shape. If the atmospheric pressure is equal to $76 \mathrm{~cm}$ of mercury, what will be the height raised in the barometer tube. The contact angle of mercury with glass $=135^{\circ}$ and surface tension of mercury $=0.465 \mathrm{~N} / \mathrm{m}$. Density of mercury = $13600 \mathrm{~kg} / \mathrm{m}^{3}$. Solution:...
Read More →The lower end of a capillary tube is immersed in mercury.
Question: The lower end of a capillary tube is immersed in mercury. The level of mercury in the tube is found to be $2 \mathrm{~cm}$ below the outer level. If the same tube is immersed in water, up to what height will the water rise in the capillary? Solution:...
Read More →The capillaries shown in figure have inner radius
Question: The capillaries shown in figure have inner radius $0.5 \mathrm{~mm}, 1.0 \mathrm{~mm}$ and $1.5 \mathrm{~mm}$ respectively. The liquid in the beaker is water. Find the heights of water level in the capillaries. The surface tension of water is $7.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$. Solution:...
Read More →Consider a small surface area of
Question: Consider a small surface area of $1 \mathrm{~mm}^{2}$ at the top of a mercury drop of radius $4.0 \mathrm{~mm}$. Find the force exerted on this area (a) by the air above it (b) by the mercury below it and (c) By the mercury surface in contact with it. Atmospheric pressure $=1.0 \times 10^{6} \mathrm{~Pa}$ and surface tension of mercury $=0.465 \mathrm{~N} / \mathrm{m}$. Neglect the effect of gravity. Assume all numbers to be exact. Solution:...
Read More →Find the excess pressure inside
Question: Find the excess pressure inside (a) a drop of mercury of radius $2 \mathrm{~mm}$ (b) soap bubble of radius $4 \mathrm{~mm}$ and (c) An air bubble of radius $4 \mathrm{~mm}$ formed inside a tank of water. Surface tension of mercury, soap solution and water are $0.465 \mathrm{~N} / \mathrm{m}, 0.03 \mathrm{~N} / \mathrm{m}$ and $0.076 \mathrm{~N} / \mathrm{m}$ respectively. Solution:...
Read More →A 5.0 cm long straight piece of thread is kept on the surface of water.
Question: A $5.0 \mathrm{~cm}$ long straight piece of thread is kept on the surface of water. Find the force with which the surface on one side of the thread pulls it. Surface tension of water $=0.076 \mathrm{~N} / \mathrm{m}$ Solution:...
Read More →A steel plate of face area
Question: A steel plate of face area $4 \mathrm{~cm}^{2}$ and thickness $0.5 \mathrm{~cm}$ is fixed rigidly at the lower surface. A tangential force of $10 \mathrm{~N}$ is applied on the upper surface. Find the lateral displacement of the upper surface with respect to the lower surface. Rigidity modulus of steel $=8.4 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$. Solution:...
Read More →Estimate the change in the density of water in ocean at
Question: Estimate the change in the density of water in ocean at a depth of $400 \mathrm{~m}$ below the surface. The density of water at the surface $=1030 \mathrm{~kg} / \mathrm{m}^{3}$ and the bulk modulus of water $=2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$. Solution:...
Read More →Find the increase in pressure required to decrease
Question: Find the increase in pressure required to decrease the volume of a water sample by $0.01 \%$. Bulk modulus of water = $2.1 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$ Solution:...
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Question: If $\mathrm{A}$ is an invertible square matrix and $\mathrm{k}$ is a non-negative real number then $(\mathrm{KA})^{-1}=$ ? A. $\mathrm{K} \cdot \mathrm{A}^{-1}$ B. $\frac{1}{k} \cdot A^{-1}$ c. $-\mathrm{k} \cdot \mathrm{A}^{-1}$ D. None of these Solution:...
Read More →A copper wire of cross-sectional area
Question: A copper wire of cross-sectional area $0.01 \mathrm{~cm}^{2}$ is under a tension of $20 \mathrm{~N}$. Find the decrease in the cross-sectional area. Young's modulus of copper $=1.1 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ and Poisson's ratio $=0.32\left[\right.$ Hint: $\left.\frac{\Delta \mathrm{A}}{\mathrm{A}}=2 \frac{\Delta \mathrm{r}}{\mathrm{r}}\right]$ Solution:...
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Question: If $A$ is a 2-rowed square matrix and $|A|=6$ then $A \cdot \operatorname{adj} A=$ ? A. $\left(\begin{array}{ll}6 0 \\ 0 6\end{array}\right)$ B. $\left(\begin{array}{ll}3 0 \\ 0 3\end{array}\right)$ C. $\left(\begin{array}{ll}3 0 \\ 0 3\end{array}\right)$ D. None of these Solution:...
Read More →A steel wire of original length
Question: A steel wire of original length $1 \mathrm{~m}$ and cross-sectional area $4.00 \mathrm{~mm}^{2}$ is clamped at the two ends so that it lies horizontally and without tension. If a load of $2.1 \mathrm{~kg}$ is suspended from the middle point of the wire, what would be its vertical depression? $\mathrm{Y}$ of the steel $=2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$. Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ Solution:...
Read More →A sphere of mass 20 kg is suspended by a metal wire of
Question: A sphere of mass $20 \mathrm{~kg}$ is suspended by a metal wire of unstretched length $4 \mathrm{~m}$ and diameter $1 \mathrm{~mm}$. When in equilibrium, there is a clear gap of $2 \mathrm{~mm}$ between the sphere and the floor. The sphere is gently pushed aside so that the wire makes an angle $\theta$ with the vertical and is released. Find the maximum value of $\theta$ so that the sphere does not rub the floor. Young's modulus of the metal of the wire $2.0 \times 10^{11} \mathrm{~N} ...
Read More →Solve this following
Question: If $A=\left(\begin{array}{ll}1 4 \\ 2 3\end{array}\right)$ then $A^{2}-4 A=$ ? A. 1 B. 51 C. 31 D. 0 Solution:...
Read More →Consider the situation shown in figure.
Question: Consider the situation shown in figure. The force $\mathrm{F}$ is equal to the $\mathrm{m}_{2} \mathrm{~g} / 2$. If the area of cross-section of the string is A and its Young's modulus Y, find the strain developed in it. The string is light and there is no friction anywhere. Solution:...
Read More →A steel rod of cross-sectional area
Question: A steel rod of cross-sectional area $4 \mathrm{~cm}^{2}$ and length $2 \mathrm{~m}$ shrinks by $0.1 \mathrm{~cm}$ as the temperature decreases in night. If the rod is clamped at both ends during the day hours, find the tension developed in it during night hours. Young's modulus of steel = $1.9 \times 10^{11} \mathrm{~N} / \mathrm{m} 2$. Solution:...
Read More →Solve this following
Question: If $A=\left(\begin{array}{cc}1 2 \\ 4 -3\end{array}\right)$ and $f(x)=2 x^{2}-4 x+5$ then $f(A)=$ ? A. $\left(\begin{array}{cc}19 -32 \\ -16 51\end{array}\right)$ B. $\left(\begin{array}{cc}19 -16 \\ -32 51\end{array}\right)$ c. $\left(\begin{array}{cc}19 -11 \\ -27 51\end{array}\right)$ D. None of these Solution:...
Read More →Two persons pull a rope towards themselves.
Question: Two persons pull a rope towards themselves. Each person exerts a force of $100 \mathrm{~N}$ on the rope. Find the Young's modulus of the material of the rope if it extends in length by $1 \mathrm{~cm}$. Original length of the rope $=2 \mathrm{~m}$ and the area of cross-section $=2 \mathrm{~cm}{ }^{2}$. Solution:...
Read More →The two wires shown in figure are made of the same material
Question: The two wires shown in figure are made of the same material which has a breaking stress of $8 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$. The area of cross-section of the upper wire is $0.006 \mathrm{~cm}^{2}$ and that of the lower wire is $0.003 \mathrm{~cm}^{2 \cdot}$ The mass $\mathrm{m}_{1}=10 \mathrm{~kg}, \mathrm{~m}_{2}=20 \mathrm{~kg}$ and the hanger is light. (a) Find the maximum load that can be put on the hanger without breaking a wire. Which wire will break first if the lo...
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