A bar magnet makes 40 oscillations per minute in an oscillation magnetometer.
Question: A bar magnet makes 40 oscillations per minute in an oscillation magnetometer. An identical magnet is demagnetized completely and is placed over the magnet in the magnetometer. Find the time taken for 40 oscillations by this combination. Neglect any induced magnetism. Solution:...
Read More →Find the largest possible area of a right-angles triangle whose hypotenuse is
Question: Find the largest possible area of a right-angles triangle whose hypotenuse is $5 \mathrm{~cm}$. Solution:...
Read More →Solve this following
Question: A wire of length $36 \mathrm{~cm}$ is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum. Solution:...
Read More →An open tank with a square base and vertical sides is to be constructed from a metal
Question: An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of the material will be least when the depth of the tank is half ofits width. Solution:...
Read More →Solve this following
Question: A square piece of tin of side $18 \mathrm{~cm}$ is to be made into a box without the top, by cutting a square piece from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum? Also, find the maximum volume of the box. Solution:...
Read More →A square tank of capacity 250 cubic meters has to be dug out.
Question: A square tank of capacity 250 cubic meters has to be dug out. The cost of the land is Rs. 50 per square metre. The cost of digging increases with the depth and for the whole tank, it is Rs. $\left(400 \times h^{2}\right)$, where $h$ metres is the depth of the tank. What should be the dimensions of the tank so that the cost is minimum? Solution:...
Read More →Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius
Question: Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius $5 \sqrt{3} \mathrm{~cm}$ is $(500 \pi) \mathrm{cm}^{3}$. Solution:...
Read More →A short magnet oscillates in an oscillation magnetometer with
Question: A short magnet oscillates in an oscillation magnetometer with a time period of $0.10$ s where the earth's horizontal magnetic field is $24 \mu \mathrm{T}$. A downward current of $18 \mathrm{~A}$ is established in a vertical wire placed $20 \mathrm{~cm}$ east of the magnet. Find the new time period. Solution:...
Read More →The combination of two bar magnets makes 10 oscillations per second
Question: The combination of two bar magnets makes 10 oscillations per second in an oscillation magnetometer when like poles are tied together. Find the second when unlike poles are tied together. Find the ratio of the magnetic moments of the magnets. Neglect any induced magnetism. Solution:...
Read More →A bar magnet takes
Question: A bar magnet takes $\pi / 10$ second to complete oscillation in an oscillation magnetometer. The moment od inertia of the magnet about the axis of rotation is $1.2 \times 10^{-4} \mathrm{~kg}-\mathrm{m}^{2}$ and the earth's horizontal magnetic field is $30^{\mu} \mathrm{T}$. Find the magnetic moment of the magnet. Solution:...
Read More →A deflection magnetometer is placed with its arms in north-south direction.
Question: A deflection magnetometer is placed with its arms in north-south direction. How and where should a short magnet having $\frac{M}{B_{H}}=40 \mathrm{~A}-\mathrm{m}^{2} / T$ be placed so that the needle can stay in any position? Solution:...
Read More →The magnetometer of the previous problem is used
Question: The magnetometer of the previous problem is used with the same magnet in Tan-B position. Where should the magnet be placed to produce a $37^{\circ}$ deflection of the needle? Solution:...
Read More →Two sides of a triangle have lengths
Question: Two sides of a triangle have lengths $a$ and $b$ and the angle between them is $\theta$. What value of $\theta$ will maximize the area of the triangle? Solution:...
Read More →A short magnet produces a deflection of
Question: A short magnet produces a deflection of $37^{\circ}$ in a deflection magnetometer in Tan-A position when placed at a separation of $10 \mathrm{~cm}$ from the needle. Find the ratio of the magnetic moment of the magnet to the earth's horizontal magnetic field. Solution:...
Read More →A moving-coil galvanometer has a 50-turn coil of size 2cm×2cm.
Question: A moving-coil galvanometer has a 50 -turn coil of size $2 \mathrm{~cm} \times 2 \mathrm{~cm}$. It is suspended between the magnetic poles producing a magnetic field of $0.5 \mathrm{~T}$. Find the torque on the coil due to the magnetic field when a current of $20 \mathrm{~mA}$ passes through it. Solution:...
Read More →A tangent galvanometer shows a deflection of
Question: A tangent galvanometer shows a deflection of $45^{\circ}$ when $10 \mathrm{~mA}$ of current is passed through it. If the horizontal component of the earth's magnetic field is $B_{H}=3.6 \times 10^{-5} \mathrm{~T}$ and radius of the coil is $10 \mathrm{~cm}$, find the number of turns in the coil. Solution:...
Read More →The needle of a dip circle shows an apparent dip of
Question: The needle of a dip circle shows an apparent dip of $45^{\circ}$ in a particular position and $53^{\circ}$ when the circle is rotated through $90^{\circ}$. Find the true dip. Solution:...
Read More →A rectangle is inscribed in a semicircle of radius
Question: A rectangle is inscribed in a semicircle of radius $r$ with one of its sides on the diameter of the semicircle. Find the dimensions of the rectangle so that its area is maximum. Find also this area. Solution:...
Read More →A magnetic needle is free to rotate in a vertical plane
Question: A magnetic needle is free to rotate in a vertical plane which makes an angle of $60^{\circ}$ with the magnetic meridian. If the needle stays in the direction making an angle of $\tan ^{-1}(2 / \sqrt{3})$ with the horizontal, what would be the dip at that place? Solution:...
Read More →The magnetic field due to the earth has a horizontal component of
Question: The magnetic field due to the earth has a horizontal component of $26 \mu$ Tat a place where the dip is $60^{\circ}$. Find the vertical component and the magnitude of the field. Solution:...
Read More →If the earth's magnetic field has a magnitude
Question: If the earth's magnetic field has a magnitude $3.4 \times 10^{-5} \mathrm{~T}$ at the magnetic equator of the earth, what would be its value at the earth's geomagnetic poles? Solution:...
Read More →The magnetic moment of the assumed dipole at the earth's
Question: The magnetic moment of the assumed dipole at the earth's center is $8.0 \times 10^{22} \mathrm{~A}-\mathrm{m}^{2}$. Calculate the magnetic field B at the geomagnetic poles of the earth. Radius of the earth is $6400 \mathrm{~km}$. Solution:...
Read More →Show that the surface area of a closed cuboid with square base and given volume is minimum when it is a cube.
Question: Show that the surface area of a closed cuboid with square base and given volume is minimum when it is a cube. Solution:...
Read More →A magnetic dipole of magnetic moment
Question: A magnetic dipole of magnetic moment $0.72^{\sqrt{2}} \mathrm{~A}-\mathrm{m}^{2}$ is placed horizontally with the north pole pointing towards east. Find the position of the neutral point if the horizontal component of the earth's magnetic field is $18 \mu T$. Solution:...
Read More →A magnetic dipole of magnetic moment
Question: A magnetic dipole of magnetic moment $0.72 \mathrm{~A}-\mathrm{m}^{2}$ is placed horizontally with the north pole pointing towards south. Find the position of the neutral point if the horizontal component of the earth's magnetic field is $18 \mu \mathrm{T}$. Solution:...
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