Physics-
General
Easy
Question
A cube of aluminium of sides 0.1 m is subjected to a sharing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be
- 0.02
- 0.1
- 0.005
- 0.002
The correct answer is: 0.002
Shearing strain = ![fraction numerator 0.02 blank cross times 10 to the power of negative 2 end exponent over denominator 0.1 blank end fraction equals 0.002](data:image/png;base64,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)
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physics-
A uniform slender rod of length L, cross-sectional area A and Young’s modulus Y is acted upon by the forces shown in the figure. The elongation of the rod is
![](data:image/png;base64,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)
A uniform slender rod of length L, cross-sectional area A and Young’s modulus Y is acted upon by the forces shown in the figure. The elongation of the rod is
![](data:image/png;base64,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)
physics-General
physics-
The graph shows the behaviour of a length of wire in the region for which the substance obeys Hooke’s law.
and
represent
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/485582/1/900243/Picture7.png)
The graph shows the behaviour of a length of wire in the region for which the substance obeys Hooke’s law.
and
represent
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/485582/1/900243/Picture7.png)
physics-General
physics-
If the shear modulus of a wire material is 5.9
then the potential energy of a wire of
in diameter and 5 cm long twisted through an angle of 10’ , is
If the shear modulus of a wire material is 5.9
then the potential energy of a wire of
in diameter and 5 cm long twisted through an angle of 10’ , is
physics-General
physics-
The Young’s modulus of the material of a wire is equal to the
The Young’s modulus of the material of a wire is equal to the
physics-General
Maths-
Maths-General
physics-
Two short bar magnets of equal dipole moment M are fastened perpendicularly at their centers, figure. The magnitude of resultant of two magnetic field at a distance
from the center on the bisector of the right angle is
![](data:image/png;base64,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)
Two short bar magnets of equal dipole moment M are fastened perpendicularly at their centers, figure. The magnitude of resultant of two magnetic field at a distance
from the center on the bisector of the right angle is
![](data:image/png;base64,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)
physics-General
physics-
Two magnets of equal mass are joined at 90
each other as shown in figure. Magnet
has a magnetic moment
times that of
. The arrangement is pivoted so that it is free to rotate in horizontal plane. When in equilibrium, what angle should
make with magnetic meridian?
![](data:image/png;base64,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)
Two magnets of equal mass are joined at 90
each other as shown in figure. Magnet
has a magnetic moment
times that of
. The arrangement is pivoted so that it is free to rotate in horizontal plane. When in equilibrium, what angle should
make with magnetic meridian?
![](data:image/png;base64,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)
physics-General
physics-
The pressure applied from all directions on a cube is
. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is
and the coefficient of volume expansion is ![alpha](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAKCAYAAACALL/6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAJVJREFUeNpjYEAFwkC8EIh/QGkeJDkQPxRZMRsQHwViLyh7PxBPgcrJA/E5NMMZaoG4EolvAMR3oeylQGyLruExmhNA4CAQuwHxNHTFxkB8mAETJAPxcSwGgT2zHIuGhVB/YYAgIF6HJjYbiBOhNquga+AD4vtArAbEgkA8H4hnQuW2QQMEA8hDg/IcWnjHA/ElBnIBAHRLGk6b6b/RAAAAT3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT4mI3gzQjE7PC9taT48L21hdGg+O57raQAAAABJRU5ErkJggg==)
The pressure applied from all directions on a cube is
. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is
and the coefficient of volume expansion is ![alpha](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAKCAYAAACALL/6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAJVJREFUeNpjYEAFwkC8EIh/QGkeJDkQPxRZMRsQHwViLyh7PxBPgcrJA/E5NMMZaoG4EolvAMR3oeylQGyLruExmhNA4CAQuwHxNHTFxkB8mAETJAPxcSwGgT2zHIuGhVB/YYAgIF6HJjYbiBOhNquga+AD4vtArAbEgkA8H4hnQuW2QQMEA8hDg/IcWnjHA/ElBnIBAHRLGk6b6b/RAAAAT3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT4mI3gzQjE7PC9taT48L21hdGg+O57raQAAAABJRU5ErkJggg==)
physics-General
physics-
A wire
has length 1 m and cross-sectional area 1
The work required to increase the length by 2 mm is
A wire
has length 1 m and cross-sectional area 1
The work required to increase the length by 2 mm is
physics-General
physics-
The diagram shows a force-extension graph for a rubber band. Consider the following statements
I. It will be easier to compress this rubber than expand it
II. Rubber does not return to its original length after it is stretched
III. The rubber band will get heated if it is stretched and released
Which of these can be deduced from the graph
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/485549/1/900159/Picture9.png)
The diagram shows a force-extension graph for a rubber band. Consider the following statements
I. It will be easier to compress this rubber than expand it
II. Rubber does not return to its original length after it is stretched
III. The rubber band will get heated if it is stretched and released
Which of these can be deduced from the graph
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/485549/1/900159/Picture9.png)
physics-General
physics-
A wire of length Land radius
rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is
If another wire of same material but of length 2L and radius
is stretched with a force 2F, the increase in its length will be
A wire of length Land radius
rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is
If another wire of same material but of length 2L and radius
is stretched with a force 2F, the increase in its length will be
physics-General
physics-
The variation of intensity of magnetization
with respect to the magnetizing field (H) in a diamagnetic substance is described by the graph in figure.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHIAAACRCAYAAAAfDexRAAAR3ElEQVR4nO2dfVBUVR+AH/xgNgZErWBjLDTko0SsQRoqGiH+kBxTV6PEUGnQGqWUEsxUpLTSRC1NYlIZDMlMSww186OkAYLRBQplZtklcyeFNRxhA3VF675/8O4G8r0se3cv+8zsCIf78cOHc+655/7OuU6CIAg4sHsGiR2AA8vgECkRHCIlgkOkRHCIlAgOkRLBIVIiOERKBIdIieAQKREcIiWCQ6REcIiUCA6RZlJaWoqTk1ObT15enmjxOESaSXBwMKdPnyY+Ph5BEDh9+jTTp0+ntrZWlHgcIvvAL7/8wrRp0wCYOHGiqLE4OR4sm4+fnx9lZWU0NjayZcsWANLS0kSJxSHSTNRqNf7+/qbv9+zZQ2xsrGjxOJpWM/nmm2/47rvvEAQBpVLJ3LlzKS0tFS0eh0gz2b17t+n6GBwcjK+vLyUlJaLFM0S0M9sxOTk5xMXFAVBbW8uWLVvQaDTMnDlTvKAEB91SW1srZGRkCIIgCAqFQgDafMLCwoTTp0+LGqNDZDekpqYKMplMeOGFF8QOpUscvdZOyM/PZ86cOej1egYNGoRGo0Eul4sdVqeY1dkpLS0lOTmZ9PT0dj8zGAxt/rU3dDodzz77rGmURiaTkZqaatMSga6vkQqFosPysLAwARC2b9/epvyrr74SEhMThY8//lhYv369pVoNq3Dz5k3h7bffFoYNG9bm+hcQECDcvHlT7PC6xaxea0FBQYc9NIPBQENDA+7u7n364xKDX3/9laNHj/Lvv/8yZMgQ7ty5g4eHBxkZGchkMrHD6xbHfeT/CQ0N5dSpUzg5OTF06FCGDBlCREQE4eHhYofWI9qJbP1YJjc31/S1qPdIVuDKlSv4+/uzcOFC4uLiGDJkCJ988onYYfWYdk2r0KoTO3PmTA4ePGjVgMTAKDE+Pp7NmzeTn59PVFSU7XdwWjHgR3bulgjYTXPaGrOvkXV1dej1ekvGYnU6kmivdFkjO2tWZ86cSWFhIYWFhbi7u5OQkNAvwfUnUpIIZjat9n7d1Gq1BAYG8uqrr0pCIgzA2w+jxMTERMlIhAEm0igxOTmZdevWiR2ORRkwIltLXLNmjdjhWJwBIVLqEmEAiLQXiWq1mpycHLP3l7RIe5EIEB8fz6hRo8zeX7Ii7Ulieno6/v7+uLm5mX0MSYq0J4mlpaWEhoZy7dq1Ph1HciIrKip49NFH7UJiU1MTJSUlBAcHU1dXR3BwsNnHkpTIiooKnnzySdLS0mxeIsC8efN4/fXXcXJyorCwsE/HkozI1hIXL14sdjjdkpeXx4YNGxBaMhn7fDxJPMayFYkqlQqdTkdJSQm//fYbKpUKmUxGcXFxm+1ycnIYNWoUfn5+QEvGXlhYWN9ObskEoKysLCEuLk5ITU0VUlNTLXnoTikoKBBcXFyE9PR0q5yvNX/88YcQGhoqjBkzRgAENzc3wdXVVQCEQYMGCXK5XCgvL2+zjzHB2ZjYtn37dlOiV2fJbj3BrmtkYWEhkydPFq0myuVy/Pz8OHfuHACNjY0ADB8+nKCgIL777juGDx/eZp+7nxwlJCRY5DGg3V4jjRI/++wz0ZrToqIiKisruXnzpqnsvvvu47XXXuPnn39uJ7E/sUuRrSXOnz/f6uf/6KOP8PDwYOrUqYwZM4a33noLAA8PDw4cOMCGDRusHpPdiRRLok6nIyYmBmdnZ7Zu3cobb7zBzZs3OXDgAHq9ntDQUKqqqkTL97Gra6QYEo8ePcrq1as5d+4cQUFB/PTTT+16mGvXrhU9485uaqS1JaakpODh4cGsWbN45JFHuHr1KmVlZR3eJogtEexEpLUk6nQ6ZsyYgbOzM1lZWaxcuRKDwcDevXut2nExB5sXaQ2JR48eJSgoiAcffJDLly9TVFTEpUuXSExM7Jfz9Qc2fY3sb4kpKSlkZGRw48YNoqOjOXPmjF1M2OkIm62R/SVRq9UydepUnJ2dyc7OZvXq1dy4cYMvvvjCbiWCjYrsD4m5ubk8+uij+Pj4cP36dYqKitBqtXbVfHaFzTWt33//PbNmzSIrK4vZs2f36VgGg4F3332XHTt2YDAYmD9/PmVlZXZd8zrDpkQeOnSImJgYvv32W6ZMmWL2cbRaLQkJCZw4cYJRo0axdetW5s6da8FIbQ+baVq//vprZs+e3SeJubm5BAQEMHbsWK5fv45SqeTChQuSlwg2UiO//vpr4uLiOHnyJM8880yv9jUYDKxatYrMzEz++ecfYmNj+fXXXyXZfHaF6DXSKPHEiRO9klhVVUVUVBRubm7k5eXx6aef0tjYaDdz/i2NqCLNkbhv3z58fX0ZP348AJWVlWg0mgHRfHaFaCJ7I9FgMLBs2TJcXV157bXXeO6552hubuaHH34wpUsMdEQR2VOJFRUVbZrPnJwc9Ho927Zts2K09oHVRfZEYnZ2Nr6+vqblpaurq9FoNMyYMcOaodoVVhXZlUSDwcCSJUtwdXXlzTffbNN8ent7WzNMq5Gent5u+ZvWZb25bFjt9qMziRUVFSxZsoSioiJ8fHzYv39/nwYD7ImEhATTghorV65sU3bhwgV27drV42NZpUZ2JHHnzp14e3szceJERowYQXV1NSqVasBINHLs2DFeeeWVdmXLly/v1XF6XCNra2vJyspCqVQycuRIYmNje5Sf0lpiSEgICxYs4KuvvsLFxYXFixfz3nvv9SpgKWF8R8gDDzzQpuzKlSu97o33qEbm5eUxadIk3N3dWbVqFdOmTSMiIoL8/Pwu9zNKzMjI4J133mHYsGEUFxeTl5dHXV2dpCS+//77xMTEsHv3bnQ6XY/2+fHHHyksLGyzbJyXl5dpme1e0V0Gs1KpFAChqqqqTfkHH3wgxMfHtylrnWn+wgsvCEOHDhU8PT0FZ2dnITo6WtDpdGZnUts65eXlwuDBgwVXV1fBxcVF8Pb2FhYuXCjk5uZ2ukyor6+vUFNT06YsLCys3f91T+i2aY2JiWH79u3tqrq7u3unc/qOHj2KUqlk0KBB3Lp1Cy8vL86ePUtoaGjv/9LsiMGDB9PU1AS0PIHZuXMn+/fvR6/X4+fnR1pamunNBGq1Gk9PT4s0q9DNNTIvLw+NRtPhw93y8nJ8fHw63G/ChAkolUoEQcDNzY3nnntuQIzArFmzhubmZtP3w4YNQ6/XExQUhEKhICgoyPSzjRs3kpyc3Gb/rKws85pV6LppTUpK6nBiSU1NjQC0W1m/ddOamJgouLq6ChMmTBDuueceQS6Xt1txWUps27ZNGDx4sGnV5aSkJOHYsWMdbkurFZqVSqUgCC3N7N1lvaHLGllfX99heUpKCmFhYV32Wt3d3Tl//jyBgYGsWLECmUzGunXrSE5OJiYmhs2bN9t8imFvGD9+PEeOHCEqKqrbbYUO5kOq1eo+nb/LXmt4eDi5ubmmdh8gOTmZzMxMMjMzuz24t7c358+fJy0tDYPBgE6n4/Dhw5SUlODh4UFkZCRVVVV9+gVshfDw8B5J7C+6FBkbG4tCocDNzY2ZM2fi5OREfX09NTU1Pb7mtZa5du1aIiMjTY+eXFxcGD9+PAEBAeTm5lrkFxqodNtrPXjwIGq1msbGRrKzs3F1de31SYwyAwMDgZZOgbe3N4cPHwZg0aJFzJ07F5lMxtKlS0lJSen1OQY6PRoQ8PPzIzg42CyJRlrXzGXLlrX5WUZGBk1NTWzYsIFdu3Yhk8mIjo6moaHB7PMNNKz69MMoMzMzs51MgAULFqDVajl16hRarZb777+f0NBQKioqrBmmXWL155He3t5UVVV1KhMgLCyMM2fOcOnSJR5++GEmTpyIt7c32dnZVo7WfhAlQ8DT07Nbmcbt9u7dS3NzM3PmzGHp0qW4u7t3uc9ARbScnZ7KNLJ+/Xrq6+vZsWMHeXl5DB06FIVCgVartUK0to+oWXS9lQnw0ksvodFoKC0t5erVq/j6+hIUFNTnlaPsHdHzWs2RCRAUFERBQQF//fUXTzzxBJGRkXh5ednV23MsiegiwXyZ0LKmza5du7h16xaJiYls2LABFxcXFi1aZLevPjQHmxAJLTIvXrzIl19+aXZnZvny5aZhwNOnT+Pm5kZERESfxzHtAZsRCS21S6VS9UkmQGRkJCqVisrKSlxdXRk3bhwBAQEcOnTIgtHaFjYlEiwnE1pGpA4fPszt27eJiIggNjaWe++9l9TUVAtFazvYnEiwrEwjxmHAdevWsXv3bpydnZk/f75khgFtUiT0j0yAxYsXo9VqKSoq4ty5c9x33308+eSTnD171mLnEAObFQltZcbGxlr02CEhIZSVlXH58mXkcjlPP/00Dz/8cK+Sgm0JmxYJ/8k8fvx4v8z98PT0JDc3l+bmZl566SWSk5Nxc3NjyZIlFj9Xf2LzIqFF5p9//olSqezXiTzGYcBdu3Zx5MgRnJ2def755+1iGNAuRALIZDKqq6v7XSa0DANeuHABpVJJfX09Y8eOZcKECTY9DGg3IsG6MgHTGG5dXR3jxo0zDQNu3LixzXZ79uyhpKSk3+PpCrsSCdaXCS1N+969e03DgJs3b+aee+5hwYIFGAwGfv/9dyZNmsT69eutEk9H2J1IEEemkeXLl3PlyhW+/fZbiouLcXNzMy1/tmnTJqKiono8xpufn096erppDk1paanZcdmlSBBXJsCUKVOorKykuLiY+vp6/v77b65du8ZPP/1EUFAQFy9e7HRftVqNn5+fKcnsl19+ITk5mePHj5sdj92KhP9klpeXiyJTp9MRERHB7du3TWW3b99Go9EQEhLCgQMH2u2jVqvx9/dn06ZNFBQUkJCQwMqVKxkxYoQpy9Ac7FoktMjUarVUVlZaXaZcLufkyZOkpKSQlJTEY489xtChQ3F1dcVgMPDiiy+yatWqNvusWLGC+Ph402QeI5MnTyYkJMTsWGxi5StLoNFo8PX1ZcaMGVZ9yhEaGtpulplOp0OlUqFSqWhoaMBgMCCTyVCr1eTm5naYXd+XF5yBhESCeDLvRi6XI5fL282NOXPmDEC/zEyz+6b1bjQajSjNrNhITiTYrszIyEigZd5pa5qamkzrCZiLpJrW1hib2alTp3LkyBGxwwFaFn3Yvn0706dPJykpidGjR6PX66mvr+/zw25J1kgjGo2G6upq0d6O0xEJCQlUVVUxevRoAJ566inS0tL6NK8GJFwjjahUKh5//HHCw8O7XYXEWvj5+Vm8wyPpGmmkvLwcvV5vUzXT0gwIkSB9mQNGJPwnsy8jKLbKgBIJLTLv3LnD448/LnYoFmXAiYQWmYCkZA5IkdAiUyaTSUam2SL7OhJhCxQXF+Pu7i4Jmb0WmZ6ejp+fX7u3d9sr+fn5kpDZa5F6vR6NRtMfsYiGFGT2WuTKlStRKBT9EYuo3C3TYDCwb98+kaPqOQO2s9MRrWVevHiRmJgYu5mKJ/mx1t6Sn59PeHg4Tz31FDKZjPj4eKKiotq9pikvL4/du3ebvh85ciTTpk1rl8JhLTqtkU1NTZSWlpo+A4Xo6GgqKytpbm7GYDDQ3NzM6tWr220XEhJCXV0dPj4+puXBp0+fzocffihC1F2IrKmp4YMPPjB9Bgovv/wyTk5O3Lp1C2j5g96xY0e7dcqNKx8vXLiQ4OBgpk2bhlKpZNWqVaLcmnUq0niLYfwYUavVnD9/nvLyckncS97NjBkzUKvVzJs3D3d3dwAaGxuZM2dOm+06WrbamEBVU1NjvYD/T687O9988w2BgYFcu3bN7ieHdsbw4cPJzMwkPz+fwMBARowYQXFxcZvnmT/++KP5y1b3A73u7BjfGDMQeOyxxzh37hz79u3j1VdfJS4uDpVKhUwm4/PPP2f//v1ttjeuHuLl5WX1WC3aaw0ICMBgMCCXyy15WNGZPXs2UVFRbNq0iYaGBtNS1q3fEAAtyccKhaJduTVwEjpaYNtBl3z44Yc89NBDpunwtbW1pKSkUFVVxbFjx/qcf2MWZi+rP0BRKBQCIISFhQkKhcL0doCkpCShsbFRtLgcNbKXdHRP3dd0f0vgECkRHGOtEsEhUiI4REoEh0iJ4BApERwiJYJDpERwiJQIDpESwSFSIjhESgSHSInwP0LWmqUfcYGKAAAAAElFTkSuQmCC)
The variation of intensity of magnetization
with respect to the magnetizing field (H) in a diamagnetic substance is described by the graph in figure.
![](data:image/png;base64,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)
physics-General
Maths-
The number of one one onto functions that can be defined from A={a,b,c,d} into B={1,2,3,4} is
The number of one one onto functions that can be defined from A={a,b,c,d} into B={1,2,3,4} is
Maths-General
maths-
The number of ways one can arrange words with the letters of the word ’ so that ↑MADHURI↑ always vowels occupy the beginning, middle and end places is
The number of ways one can arrange words with the letters of the word ’ so that ↑MADHURI↑ always vowels occupy the beginning, middle and end places is
maths-General
Maths-
If
defined by ![f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x squared plus 1 end fraction comma text then end text f text is end text](data:image/png;base64,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)
If
defined by ![f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x squared plus 1 end fraction comma text then end text f text is end text](data:image/png;base64,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)
Maths-General