Physics-
General
Easy
Question
A uniform disc of mass M and radius R is supported vertically by a pivot at its centre as shown. A small dense object of mass M is attached to the rim and raised to the highest point above the centre. The unstable system is then released. The angular speed of the system when the attached object passes directly beneath the pivot is
![](data:image/png;base64,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)
The correct answer is: ![square root of fraction numerator 8 g over denominator 3 R end fraction end root](data:image/png;base64,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)
Related Questions to study
physics-
A bar of mass M & length L is in pure translatory motion with its centre of mass velocity V. It collides with and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length 2 L ). The angular velocity of the composite bar will be.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL4AAACMCAYAAADCxhM7AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABFzSURBVHhe7Z0HWBRX18fFqF8sGHuMGguIYhBLjMqrRqy8WD9L7Mlni0bUWGPHWIJGYkElKjYMNvJGlMSOiYk9+hIrCggWioAiTcRFUPb/ce7OIii7Is4uA3t+z3Ofdc6dHTab3965M3PvucXAMCYIi8+YJCw+Y5Kw+IxJwuKbCM8fP8D5Y7448Ls/4p5LwWxEXTsB3wN/4vbDJ1KkaMPiFwJSU1OxcuVKLFiwAO7u7lizZo3e4ubmBg8PDyQnJ0tHAFKC/dDH4l28W6EZ1pxNkKISacH4xr463i1rC/e/wqRg0YbFLwRERESgY8eO+Pbbb+Ht7Y0dO3boLTt37oS9vT0uXLggHQF4fP03dP2gBEqWMEe3OXvwVIoT8afcYFvJDMVLWuEHv9tStGjD4hcC7t27h1mzZonXvDJx4kScO3dO2iLx96G7pSUc+7aDTecvcTZOqkAKvOf0RauODrCt+zGWHb0lxYs2LL7C2L9/fw5hCRJ++vTpCAkJkSKvx8nJCX///be0pRH/3/XqY/omN3T7pBUW/aZp2dXRJzDq353wjZsL2ls1x9IjLD5jZDIyMjB48GDMnj1bimiQR/y96FzbAkv8/OExpg3aOnniWWb8ts9s2PeajL/O7oa9RWMsYfEZYxMTEwMrKyt06NABaWlpUlQ+8TvVqAOXc/cQesQZHzUbAv+YB9ji1BVDXI8hNuxXtPmwEVxYfMbY+Pv7o1ixYqhSpQpiY2OlqJzi14LzyYdA4gUMs2uKL7/7Hp916YmfAh5DHeGNVjVZfKYA8PLyEuKXKVMGJ06ckKIyiR+wB59WqYYZR8Mzt55i17SOKF3WHB/3d0G0OjMStA1Nq1pi0aFQzRuKOCy+ghgyZIgQ38zMDPPmzZOi8oifEnQA//tRYyw6fldsP/BbhoYf1sTYjRfFdnKQNzrb2GHlH3fEdlGHxVcIT548Qf369YX4VBwcHKQaecRXP0/H46QkqNIzpEA6kh89wlPpKa76eRqSkx4hVVtfxGHxFQL176tWrZolvq2tLaKiokSdHOIzOWHxFYKrqyuKFy+eJX7p0qWxd+9eUcfiyw+LrxDo/r1Wem1ZvHixqGPx5YfFVwCRkZGif9+iRQv06NED/fv3R+3atcX4HJVKhQcPHrD4MsPiK4DQ0FDMmDED0dHRostDXRyStm/fvqKfHxcXx+LLDIuvMJydncX9fEKtVovCXR35YfEVBom/bds2aUsDiy8/LL7CYPGNA4uvMFh848DiKwwW3ziw+AqDxTcOLL6RUD0Ihf/lQCSkSgEdsPjGgcU3EiE/OaFBmwE4/Jq53Cy+cWDxjUTgjwNRpq49fIKlgA5YfOPA4huJoA3DULFhV/jelAI6YPGNA4tvJFh8ZcHiGwkWX1mw+EaCxVcWLL6RCNowFBWtHXGI5nrrgcU3Diy+kaAW37yOHdb5heLOrRAhcXDwTdyNiheJnbS8ifh3797F1q1bcxWcxdcPi28kQr2cUL60Oeo2bILmTW1ha9sYNjaN0X2CB15k0Mm7+DSGv2vXrpnHsBETWHx9faUaDSy+flh8I5Ge/BC3bgbj+rUruHLlCq5evSpK0J37SJf2IfIq/pIlS9CmTRuxf8+ePUVqkuzZ11h8/bD4CiOv4lN+TUdHR5E6fODAgRgwYIBIUaKFxdcPi68w8ir+mTNn0Lx5c9Hdadq0qVgQIjssvn5YfIWRV/GJP//8E5MmTcL27duRnp69w8Tivw4WX2G8ifj6YPH1w+IrDBbfOLD4CoPFNw4svsJg8Y0Di68wWHzjwOIrDBbfOLD4CoPFNw4svsJg8Y0Di68wWHzjwOIrDBbfOLD4CoPFNw4svsJg8Y0Di68wWHzjwOIrDBbfOLD4CmP+/PlZK6JoYfHlh8VXAAEBAWIG1Y0bN8SUQm9vb/zxxx9iksmdO3eQkJDA4ssMi68AaFVDS0tLsfIhrXRIUwrfe+89dO7cWcyj5VUP5YfFVwjDhg17ZZ3b77//XtRxV0d+WHyFQHNm33nnnSzpzc3NceDAAVEnh/hqdQaepachPfMMQmeRtLR0PMuQKk0QFl8hXLt2De+//36W+DSRPDZWk3FHDvFjrv2KqQP7oFuP7ujeXVN69vkc89x+Rmjci7QkpgKLrxBSU1NhbW2dJT6JqUUO8YMOzEb1YtUw4Jul4uyyerUbVnw7AS0+KAvboatwL0Xa0URg8RXEyJEjhfRmZmZYvHixFJVH/OCDs1G7Slv8FiEFJC56jUOVktbYeD1RipgGLL6CoNuYJH6ZMmVw7tw5KSqf+HWqtIHPrZzdmqD/TEHVUtbYfD1BipgGLL6CuHTpEooXLy76+nFxcVJUHvFvHp6PeuXqYNTCNfD03IqtWzZhpcs0tK1fETYDliFMZVpXuiy+gnj06JHIika5MLNz//59zJw5863EDzm6GJYlysCqZXt06dJZPCPo3LUbRs9bh4BYvrg1KvHx8bh48aI4rZ88eRKnTp0SqfGuX7+OoKAgXLhwIStOWcPoySahVqtFKxgREZFVtAlTHz9+jLCwMBELDw8XD3+00L8pRnW0D+1LUBYybZxeo6Ki8Pz5c1GXmJgo0nFr6+gpKkGfgfajGJXIyEg8ffpU1KlUqhzHo79L+xMPHz7M8fmyfwYSvF+/fvj666/FHR3tZ6Dv4quvvhJ/I6+MHz8eZ8+elbaoqzMHdSq3xs5rptWl0YXBxM/IyBBJTOlVF/SApl69eqhVqxYqVaokStWqVfHZZ5+J/3FUR7HKlSujQoUK4ukm/VAOHjwoWkZbW0q3rSnr1q1DUlKSaOkodXaTJk3QuHFjtGvXDoGBgfjnn39EdmGK0f60z+TJk8VnXL58eVacCt1K9PPzQ0xMDHr37p3jeL169RKy+vj4iP2076P6lStXCsHHjh0r4tr3tGrVSqT1ph9u69ats95Dr8OHDxffhaurq0j3Xa1aNfF9tGzZEnv27BHy09Pc6tWro3///hg9ejRGjRqlt9Ax6VjahoLQiG+H3deTpIhpYzDxqUUmYUhSXSxdulQMyqLcj25ubli9ejU2bNiAmzdvitZv586dIu7u7i5eHRwccOTIEdHyrVq1CitWrMgqlHL72bNn4u+RRCThDz/8gE2bNokuBLWgdGyK0f70euzYMSHW+fPnhfzaY9HtPmqR6Syya9euHMfbvXu3eA91O2g/7fvo8/j7+4v/LvoMtK/2PRs3bhSfgc5wHh4eWe+hV+33Q2c9iq1du1Z8D3Rs+rHQD4kGre3YsUMc//Lly+LHr6/Qj5y+Q+0Zg7ixbxLKFWuALZfipYhpYzDxSQy6Q7F+/Xop8iokBrVqeYVu8R0+fFjaYt6E2KCjcP1uPS7HqKSIaWMw8fft2yfEp/ztuqAWjlrQvECtFx3rFfEzW0R99yPUGWpoetcM8wKDiT9u3DghPg2tTU5OlqI5eRPxqRvzsvhqVRDWTRuFz79ahDPhmovEF6hwascSjBw+Hj9fyL7YDsMYSHy6oKWLOBK/XLlyoq+aG28rfkbi7+j5AT3iN8OIDedytOzquP9iZNMSmXVlMGVn7n+fMV0MIj5dWFlYWAjx6fG7rn75W4sf74fezerjw1q10aq3M+5mux0dut8F/7KsggrVP8LMna9ZXJYxOQwivqenJ0qUoNZWM+CKnjrmxluLH3cIDk1a4/Pho+HYqg3c/aVbdepEbHDqiT7DBqOdXQtM3RaoiTOMhEHEnzp1apb0VOiedG7IIX6nBk0xc+NuLBzQEr3mam4NpkccRL8OPfHj9k3o37oRJnqy+ExOZBefHu7QQ57s4tetW1c8rXwZWcS3tMb03QG46jESNu3H4mZmR//mtvFo138RQm4dQc8mViw+8wqyi08PWcqXLy+Eb9SoEcqWLSv+/XLKDEIe8RtistcN4L4PPrWxw49/XcHaUZ0wcu1FIPYQutjUZ/GZV5BdfBK5Zs2aYgjBwoULsWXLFjRr1kw8an8ZucSf4Hk1c+sRlg34FPbdHNHBYRB87mQ2/VG/oTOLz+SC7OLTUAMa1EUzimgRYkqPQcMFaDXvl3lr8WN90aJiNfyf+3/FdsDuySiVeXb5cOh6iCcHd73xSY1KGLE+QNQzjBaDXNwSNJ58xowZYi6pLt5WfHXKdaxZsAg/nwkX209jLmH5tInYckqaZhR/GWtdFuI/f8dothlGwmDi0/BbQ4vPMPmFxWdMEhafMUlYfMYkYfEZk4TFZ0wSFp8xSfIt/jNVAiLCopCSlvv8JxafUTL5Fj/irBs62A3GgcDcZ+2z+IySybf4oYeno8L/NMW2f15k/MoOi88omXyLf8tvNj6o0Bo7dKSrYPEZJcPiMyYJi8+YJCw+Y5K8pfh28A54OZ+NBhafUTJvJ375j+Fx8i6SHyUhKSlRZBJ+9FglMpvFsfiMgsm3+KHH5qFqMTPUtmmBdm3/BTu71mj5SUv0GrccdzLNT0nM30SU48ePi1zwmzdvFqmztRhSfEoOS0lZ6W8zpkG+xVcl3MUZv6PY/6sv9u7dJ3JlUjl86gqS1EBC/Ju3+KdPnxYZ2Nq2bSvSaFPmYC2UNZjm8B49elSKyMsXX3whUpFTSu4RI0aIyfHBwcEiy7G+VOdM4STf4r+O2Hx0dWbNmiVy2JPgJGL79u1FuhISj+bwOjs7Z639SmcAuQolpKVFHuzt7bNSopQqVQoVK1aElZWVmChPP4QTJ06I5ffpx8AUbgwmfn4ubikNOC2iMHfuXLGsPS0SQauD0HGmTJmS2Z2yQ9++fTFnzhyRtErOQt0oWpAiewa43AotVDFp0iQ+CxRyFCX+rVu3xOIPJDitFkILOdCCCVSoG0SrfVBOfW1MzkLL5nTp0uUV0SlHUI0aNcSZiH5we/fuFYsvaJf2YQonihKfoJVUaCUUkutlXFxcxFpYhoAupkn00qVLi7OO9sxC1xSUHiX7hTZT+FGc+Lqgvrih7upQ6013dZYtWyZEj46OlmqYogqLr5NnePJYhee6ejQZ6VClPMnciymMsPg6UKdGYP3EQZi64Xc8kWIvSIbvyikYO2874rmrXyhh8XWRocLPU1uglOUgnI/N2a4/izyK7hbvocfSE3rX32KUC4uvh4TLP+GTytUw2Sfniir+m79EzdoOOBJpeiuCFxVYfH2kR+O7fg3QoM8KZK0HnhYO5y510Wrijly6QExhgcV/DUG7pqF+3dbYFaK5nRl/fg0a12qG1afui22mcMLiv47Ecxj4sSUGuZ4Wm3sm2aOh40zc5tv6hRoW/7WocXBuN3zkOBvBkf4Y1sIaYzZekuqYwgqLnwdSbnihQ8tOGDNiCNraD8JxXi+60MPi54WMeLiPaCKGNDguPIjnUpgpvMguPg00CwwMhEqlEksB3b59WywN9Msvv0h7vKDQiJ9J9NVDWOayCqfDU6QIU5iRXfw9e/agVq1a8PDwwPz58+Hl5QVra2v069dP2uMFhUl8pmghu/i03Cct8Unj2kl4msxBXQT6AbwMi88UFLKLn5KS8soCz3Xq1EF4uGaBtuyw+ExBYZCLW5rRlF18Gt+eGyw+U1AYRHxPT0+ULFlSSG9mZobp06dLNTlh8ZmCwiDiU3YCCwuLrBZfl6wsPlNQGER8mtFEaUJIenNzc4SGhko1OWHxmYLCIOITTk5OQnyawE0pQnKDxWcKCoOJ7+vrK8RfsGCBFHkVFp8pKAwmfkhIiBB/3bp1UuRVWHymoDCY+JSpgFIB6hOVxWcKCoOJT2n5aKCavnw0lBzKx8dH2no9lGmNxWfkwGDi5wUS2dXVVZwdIiMjdRZKMkWD3caMGZOVO5Nh3oYCFZ+6OX369BGjOOkhl65Cw5snTJiAoUOH4saNG9K7GSb/FKj41G8PCwsT9/lpOLOuQvVUKJUfw8hBgYrPMAUFi8+YJCw+Y5Kw+IxJwuIzJgmLz5gkLD5jkrD4jEnC4jMmCYvPmCQsPmOCAP8P04gelOukMr4AAAAASUVORK5CYII=)
A bar of mass M & length L is in pure translatory motion with its centre of mass velocity V. It collides with and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length 2 L ). The angular velocity of the composite bar will be.
![](data:image/png;base64,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)
physics-General
physics-
A small particle of mass m and its restraining cord are spinning with an angular velocity
on the horizontal surface of a smooth disc as shown. The force F is slightly relaxed, r increases and
changes.
![](data:image/png;base64,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)
A small particle of mass m and its restraining cord are spinning with an angular velocity
on the horizontal surface of a smooth disc as shown. The force F is slightly relaxed, r increases and
changes.
![](data:image/png;base64,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)
physics-General
physics-
A small bead of mass m moving with velocity v gets threaded on a stationary semicircular ring of mass m and radius R kept on a horizontal table. The ring can freely rotate abut its centre. The bead comes to rest relative to the ring. What will be the final angular velocity of the system?
![](data:image/png;base64,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)
A small bead of mass m moving with velocity v gets threaded on a stationary semicircular ring of mass m and radius R kept on a horizontal table. The ring can freely rotate abut its centre. The bead comes to rest relative to the ring. What will be the final angular velocity of the system?
![](data:image/png;base64,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)
physics-General
physics-
A uniform 50 kg pole ABC is balanced in the vertical position. A 500 N horizontal force is suddenly applied at B as shown in fig. If the coefficient of kinetic friction between pole and surface is 0.3. The initial acceleration of point
is
![](data:image/png;base64,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)
A uniform 50 kg pole ABC is balanced in the vertical position. A 500 N horizontal force is suddenly applied at B as shown in fig. If the coefficient of kinetic friction between pole and surface is 0.3. The initial acceleration of point
is
![](data:image/png;base64,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)
physics-General
physics-
A uniform rod of length 1 is pivoted at point A. It is struck by a horizontal force which delivers an impulse J at a distance x from point A as shown in fig, impulse delivered by pivot is zero if x is equal to
![](data:image/png;base64,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)
A uniform rod of length 1 is pivoted at point A. It is struck by a horizontal force which delivers an impulse J at a distance x from point A as shown in fig, impulse delivered by pivot is zero if x is equal to
![](data:image/png;base64,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)
physics-General
physics-
A rod of mass m and length 1 is hinged at one of its end A as shown in fig. A force F is applied at a distance x from A. The acceleration of centre of mass (A) varies with x as
"![](data:image/png;base64,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)
A rod of mass m and length 1 is hinged at one of its end A as shown in fig. A force F is applied at a distance x from A. The acceleration of centre of mass (A) varies with x as
"![](data:image/png;base64,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)
physics-General
physics-
A uniform wheel of moment of inertia 1 as shown is pivoted on a horizontal axis through its centre so that its plane is vertical. A small mass m is stuck on the rim of the wheel as shown. The angular acceleration of the wheel when mass is at point A is
and when mass is at point B is
. Then
![](data:image/png;base64,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)
A uniform wheel of moment of inertia 1 as shown is pivoted on a horizontal axis through its centre so that its plane is vertical. A small mass m is stuck on the rim of the wheel as shown. The angular acceleration of the wheel when mass is at point A is
and when mass is at point B is
. Then
![](data:image/png;base64,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)
physics-General
physics-
A rod AB of length 1 m is placed at the edge of a smooth table as shown in fig. It is hit horizontally at point B. If the displacement of centre of mass in 1 s is
. The angular velocity of the rod is ![left parenthesis g equals 10 blank m divided by s to the power of 2 end exponent right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
A rod AB of length 1 m is placed at the edge of a smooth table as shown in fig. It is hit horizontally at point B. If the displacement of centre of mass in 1 s is
. The angular velocity of the rod is ![left parenthesis g equals 10 blank m divided by s to the power of 2 end exponent right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
A uniform rod of mass m, length l is placed over a smooth horizontal surface along y-axis and is at rest as shown in figure. An impulsive force F is applied for a small time
along at point A. The x-coordinate of end A of the rod when the rod becomes parallel to x-axis for the first time is (initially the coordinate of centre of mass of the rod is (0,0)) :
![](data:image/png;base64,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)
A uniform rod of mass m, length l is placed over a smooth horizontal surface along y-axis and is at rest as shown in figure. An impulsive force F is applied for a small time
along at point A. The x-coordinate of end A of the rod when the rod becomes parallel to x-axis for the first time is (initially the coordinate of centre of mass of the rod is (0,0)) :
![](data:image/png;base64,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)
physics-General
physics-
Moment of inertia of a triangle plane of mass M shown in the figure, about vertical axis AB is:
![](data:image/png;base64,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)
Moment of inertia of a triangle plane of mass M shown in the figure, about vertical axis AB is:
![](data:image/png;base64,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)
physics-General
physics-
The radius of gyration of solid hemisphere of mass M and radius R about an axis parallel to the diameter at a distance 3/4R from this plane is given by ( centre of mass of the hemisphere of the hemisphere lies at a height 3R/8 from the base)
![](data:image/png;base64,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)
The radius of gyration of solid hemisphere of mass M and radius R about an axis parallel to the diameter at a distance 3/4R from this plane is given by ( centre of mass of the hemisphere of the hemisphere lies at a height 3R/8 from the base)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASgAAABtCAYAAAAS5fxyAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABVDSURBVHhe7Z0JeE1X98avaKrEp6qfGvp9bfVRWrQlovWZWqr9t1rUTFFKUKVqrBqC1KyGmMdqq1pTlVARU4hZDNGaIiGNDFIiMSTE/P7vu50bFwkJ996cc7J+z3OeZO977sq5Ofu+Z++1117bAkEQBJ0iAiUIgm4RgRIEQbeIQAmCoFtEoARB0C0iUIIg6BYRKEEQdIsIlCAIukUEShAE3SICJQiCbhGBEgRBt4hACYKgW0SgBEHQLSJQgks4f/48YmNjcfjwYezZswe7d+9O9wgJCcH+/fvx999/IzExEdevX9csCDkRESjBYcTHx+PAgQNYtWoVZs+ejSFDhuCLL75Au3bt1NG5c2d0794dvXv3Rp8+fTI8evbsiS5dusDb2xtt27bF559/rmzNnTsXGzduxLFjx5Tg5QRS/wnDgmnD0bZFI3z4UT181vUbLFyzB5e1182OCJTw0FCQ1q5di/Hjxyvh6dSpkzr69u2LKVOmwN/fX/WKoqKicOrUKZw9exaXLl3C1atXce3aNfXz7oP1ly9fxoULF5CQkICYmBiEhoYqW/w7X331FTp06ICuXbsqoWPdsmXLEB4ejps3b2pXZg4OBU5DlRefhMVigeVxD/z76YLIxd8tuVHjEx+EJVzVzjQvIlBCprhx4waOHj2KFStWYMyYMapn9OmnnyoxmjlzJrZu3aoEyxVQ5ChIQUFBmDNnDnx9fdG+fXslXLw2iibFzcjEbv8RZTysYpS3JAZMWYIjx6Jw8mQswvZtQP+W1ZRolas/ECdNrlEiUMJ9OXToEEaNGqWGW+wdff311/j++++VH+nixYvaWdkPe15//fWXGlr26NEDbdq0waBBg5RwpqamamcZhGvx6PFWEWuv6TlMXndcq7TjRhLGtvGyipQ7ev4YolWaExEo4R7omA4MDFTDKX7Rp06dioMHD+LcuXPaGfrnxIkT+Pnnn5Xfi72ryZMnK7E1Aqe2TsNT1h5SpY6ztJp7uRK5GuULWFCo2peIv6JVmhARKBeSHBuKOZP8MMHPD35px0RMmT4by9dtxz/J2dtf5xCNjmg6pjmE43CO/iCjs2/fPowbNw6fffaZ8l0tWLDAZcPRh2HlsMbW3tETGL76mFaTHucx8MMXYMldFgGRKVqd+RCBciEnNozF08rJmf7x34p1sWz/Se1s18He0fDhw9GyZUs1W7Z3717tFXORkpKi/FYDBgzAJ598gtGjRysnvL64hPFtKsCSqySWHTyr1aXPgq/fs7YbD0zYrLfP4DhEoFxIdNBY5LcK0VveY7Bj5w5s3rwZW7Zswaa1KzCiWwO4W18rXPlzRKbc0N7hXOhH4uxb69atMW3aNDUsyinws3733Xdo3ry5cqwzRksfJMG3QUlYHq+A9eGXtLr0CVA9rdzwXXG/npaxEYFyIRSofFYRaj52o1ZjTwqGNy1jbXAFMXWbc78snLZnvBGFadGiRcZzIjsQChMFqlmzZsr5T2d79pKM0S3KweL2ClYdvqDVpc8yn7rW9pIHo9ZGaTXmQwTKhVCgPKwC1Xh4gFZzJ9smf6aGej3nH9BqHAsDHBkWwKEcHch6moXLbo4fP45evXqpSYFt27ZptdnBTfzS931rOyiAyZvv16O9jgmty1vPew6/HkzS6syHCJQLsQlUkxGrtZo78R/0kbXBucF3pWO77IxhYu+gcePGKmaJvhghfRhDRf+Uj4+PCi7NDsKXDVbD/Q+H+Gs1t0iIiUBY5D+3Cil/4aMX3eFWsjHCzrvGJZAdiEC5EJtANR21Tqu5zYnQpaj2XB5YClVFcMz9fQ9ZgUtPOnbsiC+//FL1EoQHw0DQiRMnomnTpvjll1+0Wtdx88IBfPxiHrgVqYr1UbfbwuJBDVCg8MsYNn8t/P064TFrW6o3eCmye1DqTESgXEj0xvH4t7VRFX7JC3Xq1MEHH3yAOtbjrf95oZA7Z/LyoL1fIBzxPOSykenTp6Nhw4ZYuHChVitkBUbOU9gZoc4FzK5k9y99lb/ymTdawH/332rt3eXEw+jbxNPaTh5DnscsKP5mS5h4dKcQgXIhFKgi1kbn7lEQRYsWRZEiz1iPInj2uRdRrU4L+C0IgiMGXwwTYMwPF91GR0drtcLDwngw9qbYq3KdEz0Fi0e2UwGbFkt+eNX4PzRt1gT/K1PcWr4VllK0SjvsjTH3cF0EyoXYwgzq+SxRUdlcPMvj/IVkXHXAOlfOxk2YMEH5mriAVnAcZ86cURMMdKIz8NNV7F/7Mzo0rIXSzxfDU08/g1cqVkeP4VOxZP5EeBXzQO5i5TF7k8ziCQ7gfj6oR4UzdPzy9OvXD//8ozlSBYezcuVKNGrUSC3/cWWuqvMJ8YiOicOFy7efZAlHN6Jn25aYsSFCqzEfIlAu5EFhBg8LcyTVr18fixcv1moEZ3Ly5EkV4MrJBz4YBOchAuVCooO+UwLVbMx6rebRYfhAixYt1Gyd4Frmz5+vQhJWr04/bER4dAwnUIzpOXLkiEqExqUajARmV5vryWxpYzn7QmdmZGRkWh1nYTizdfr0aeVEtr2fviAGLNKvYKuz2eSX3vZ+5h9KzybrGC/D99nez2yPjDWyt3k64QxOrB+pnJvVOk5AqPW9EenY/PPPP1Udh2k2m7xem03+zr/La+vfv78a1nF9me1aIyIi1PsZUpAVm6zja+wd8FzaY/pdHvezyUW39jaZaC45OfkOmzyH5zIdCu2xnj0P1vGnzSZfZx2v4UE2+Vl4Px9kk5/jbpu8L7RHu/b3iPfxbpv8zGwL/B/Y22Q7ZNthwGulSpWU748J8+6+Ttq8cuXKA22y/dqu01bHa+P94X26oy1Z27C9Tf40w6Lu9DCcQFFMPv74Y7z++usoX768WuTKRlG7dm1VZj2/tMxnzVks23lVqlRRN58JzliuUKECPD09VVqRXbt2qUbGOr7G/EdsFLVq1UqzyZS1tMmuvb1NflEY/GizWbFiRRXst3PnTnh5eaXZHDtuHM5EbECF117Dy2VfVXW0mZSUpNKa2GxWrVpVNUD6OOxtrlu3Djt27ECNGjVQpkwZ5M2bV01/c7ErQxZ4Hm14e3srm5wet9msXr26SuDGlCP2NtevX4/t27ffcZ2TJk1S57799tuq/Jr1evl36MxnhgObTV4Hz+PMls0m7VAsGYlN+zabzK7J/1PNmjVVmTaYW4o2mc7XZpOv0ya/7PY2N23apPI62dtkCEVcXFzaddIGbVE0eL02m++8846yOXbs2DSbvNfBwcFqHaS9TeaS4v/T3ibTtbAt8P9qs/nuu+8qm1zLxzbA9xcoUEC1Rf4/33jjjTSbbG/MKGpvk/9HtllmjWAdj/fff1/ddy5gZpnvpx3a4/+UbdVm84cfflAPNdp89dVX1WfkA9SMGHKIx8bOG8SDjYdQfFjm04k3mlBQWGY9e0W2JxzLTMrPg08iPrm4eJRle5v8Atxtk7M597PJxkibfBLz97ttJljfH30i6pZNayMnmbFJe4TDCTZMig3PIfbXyS8O4U+bTb5Om+wx2NtM7zp5Ds99WJu0R7sPssnPnJ5Nkhmb/OwZ2eS9up9N3mubTZazapNtjfCe2v4Ge5R84DCFDl/ntfI19oBok/c1PZusS8+m/XWyd2R/nfY22Vvk32ePzoyID8pA0BnORa3s+Qj6g8M5xp+x9ys4BhEog/DHH3+omTr6IgT9wp4ah4Vcy8fej/BoiEAZgICAAOV3o/Nf0D8ckjF3O7N3SsaIR0MESufQ50RxMko+beE2dJpzMkBE6uERgdIxFCcO6xhWIRiTYcOGqZlfszqxnY1hBYor9DntblYYqsCeE+NjBGPDDUaZ613IOoYVqJIlS6r9z8wIY57q1q2rAgIF48MwFi6LYcyYkDUMKVB0QpYoUUIFz5kNBuXVq1dPRQcL5oFBqUy1zOUxQuYxpECxZ5E/f35Uq1bNVAn/GX0uoQTmhVHqzIQga/cyjyEFasmSJWpNG5cX6G9fs4fj8OHDqufEpQ2CeeFsLB9CfBgJD8aQAsWZEVtWQa7TMjoUWSaZY7yTYH64VpEixWUvwv1xqkAlx4djw5rVCNoeinPpBNWmnjuF8KPhiImNQ3TUcYSFHUVU3K11XxnBNUh0INsEigt7jQzXXrVq1Qrz5s3TaoScwO+//65StTDyXMgYpwnUobXf48PK5VGskAcsbnnxZpM+OHjmznzOqUkxmDe8M8qUKo1K7zWD77Ch6NyqPt5v2AHL96S/eSW/0MWL387LzE0BjAynoLnSXsh5jBs3zrQz0Y7CKQJ17lgwvunWDfPX7EF8zBFM7f6BEpNGQ1dqZ9wmYedPKjF8rV4/q9m5c5HW7u9Lj+OJEh9gR/wV7azbMCdOvnz50gSK6Thsq/qNBn1pTA3CXqGQM2GqHaaXEdLHKQJ1+u8jiDh5TitZSTmMWsUtKNVsHO7+Ku5f1A95LAUwLuh2Hu0VQ+pYxecxjPC/N50qcwvlypUrTaAKFiyoEoQZDabSYO8vLCxMqxFyIhwRNG/eHMuXL9dqBHtc4yRPPoL65Yqj+7w9WoWNG5jW3hNuxd/DPrtO0HRv7v31NGZtvXdnV/Y4bOJkO4y47xsXkv70009aScjJ0FlOp7mst7wXlwhUyMJh6PjNTNxK2WZHahg+LuGOcq0naxVAVPAMlMhtQdkGQxB/1xZkjHlilkuKkoeHB9zc3NTvgwcP1s4wBgsWLFDZH2VoJ9hYtWqVcpozGZ1wG6cK1LnYA5g6sA0K5XsCng37IPTknUGVZ3fOQtFcFlRvMxgLf/0Rw/p1RdXXy6Bep28RkXiv/4mxQhSlsmXLqi94+/btVcAmU7gaZTEmh3RcY8fsiIJgz8iRIzFw4ECtJBCnClTs4e2YPnIg6lZ5WfV0Xq7fH/YatXpkM7h5lMCkZYGY1OUd6zl5Mdw/45xHzCRZuXJl1SXmDMiaNWvUotrSpUunpVHVM+wBMl86p5gF4W44ScQ85bJ92G1c44NKjcE39V+xCtCzWLRbE5Ibiej97n9QsGJ7sObmofkoZu1Nfeq34dbr6cCYEduMHb/kNuc4t/fmzdU7fEIabTgquBbu9NKgQQNJsaPhGoGyEh84EnnzPIWZgbe2ab4cEwyvQgwv0BzcN+Lg7fkvFK7RHUmZcM0w/zN38DAK7Olx/zoJzBMeBGf0mNucmzrkdFwmUCnbZ6BkKU/4H7mkykdXDEJeS36MWHNClclK37qw5CkF/8gH94Y4xGOebiPAHTsYUsD97AQhMzBlMHfuyek4RaBSEuMQHh6F2zJzGbN7N0aDblNgS346o115WPJVwg67TtCpkB9QxGJBwxFrtZqMoTPRKGN1Rgtz7zxByCzcMo2ZD7hRZ07GKQK1YUonPG7JgxqNPsf4CX4YOaA7OvUegyOJN5B6KgIr5w7BS/+ywOL+Agb/uAbxF7Su7KXjaFOxACyFX8OIeatwIjHjVCpM6maEhG5Lly5Veatkhw8hq7CNM/TAqCslHIFTBCr59DEsnjMR/fr0hu+YKVixaR+StSiAyxdO48Cendi5ex9C94Zgz59HcT71+q0XcRMJMeHYu2sbtu89iKSLdwVC2UHHuN5n7pilgA5PiRYXHpahQ4dixIgRWinn4TIflKPhTdP78gCus5o7d65WEoSsw0kVbtaaUzOsGlagmIT+t99+00r6IzAwUAWSSrS48KgwpIabgebEtmRYgdq1a5fal16PcHqYOZ4ka6LgCK5fv642XTDKrLUjMaxAcdlLbGz6OaOyGybGZ54nQXAUTDPETRdymsPcsAJF56Eel4wkJSUpn4E4xgVHw9CaadOmaaWcgUMFilPpHNYwaprr5h7l4BQrfzIeJD30KlDc+4w50wXB0XBWmA8/rqLIKThUoLj0hCrPuB9HHRkFqoWGhiIq6tayGb3AiHEuZ+FPQXAGzME/adIkrWR+DDvEo0DpLWWJn58fRo8erZUEwfFERkaq4E0jZO9wBOKDchAcijJ1KwNIBcGZMMRm9uzZWsncGFagfH19dSVQM2bMEN+T4BLCw8NzzIyeYQWKs2R68fUw8T0bDHP5CIIr6N+/vwpnMTuGFSjOFvJJoge4+cGAAQO0kiA4n5CQEHTq1EkrmZdsFajE/b/Du2Mv7DqRcdaCjBg0aJDaVy67uXbtGtq1ayc7cgguhzsccRt1M5N9AnUxGt2qF4bFrRRWHLqVxC4rMH2uv7+/VnI9XBd19uxZ1c3m8I7DTe51x9AHOeRw9hEXF6dyjNEXa+Y1etkkUFexakpvlC1WAO7FvBCgZdnMClzmwqjt7ILr7ZhRoUSJEqhbt67qbrMnxVStcsjh7IML0RknyMybFy/a0kCaj2wRqONBM9G+xzBM8WmFvE+XwcrDWRcoZgvI7hS6W7ZsUQ2FizkFQXA8Lheo62f2oesnrRAQcRZbJ7dGridfeSiB8vHxyfaUvwzMlC2rBcF5uFigUvGDTzt8PX2jKq0Z2fShBWrChAkICAjQStkDo3npJBcEwTm4VKCOrpqMNt3GIEHz6a0Z3cwqUGUQEJ65LzlzkNt2ukhISFAbYcbHx+Pbb7811BZUgiBkDpcJ1MWYHejaui38/0rEzatXcO36VfgPbWwVqJexNDQpU1uXb9q0Se1QzF1SOLTihgQ1a9ZEwYIFZU97QTAhLhOoDZO84ZGvECpWrgxPT09UerMSSj5bCLlyP4EXSr2GDsN+TduSKiM4pCpXrpwSqaJFi+LJJ59UvzPboCAI5sNlAhW+fTkG9emJHj17oqf16NWrFxpWL41ceQrhoxZfYPKiYLt99DKG+XAoSvaH7DknCObExU7yO9ns1wq5CpbDpjitIhNw9s5enHLnzo2goCDtVUEQzES2CpT/4A+tIvMsfj+Q+UAzJo53d3dPE6jSpUurqFpBEMxHtgrUniWjULdZZ4REazsLZwJGkNMpbhOo2rVra68IgmA2slWgHgbmPffy8koTqG7dummvCIJgNgwnUIQ79toEKrujyQVBcB6GFKg5c+YocaKDXLZ3EgTzYkiBCg4OhpubG0qVKiUR5IJgYgwpUFzmwkDNJk2aaDWCIJgRQwoUef7559GlSxetJAiCGTGsQDFZ16xZs7SSIAhmxLACxYyWkupEEMyNYQVKEATzIwIlCIJuEYESBEG3iEAJgqBbRKAEQdAtIlCCIOgWEShBEHSLCJQgCLpFBEoQBN0iAiUIgm4RgRIEQbeIQAmCoFtEoARB0C0iUIIg6BYRKEEQdIsIlCAIOgX4fw1k9N11B8uoAAAAAElFTkSuQmCC)
physics-General
physics-
A square plate of mass M and edge L is shown in fig. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° from horizontal is
![](data:image/png;base64,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)
A square plate of mass M and edge L is shown in fig. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° from horizontal is
![](data:image/png;base64,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)
physics-General
physics-
A circular plate of radius 1/2R is cut from one edge of a thin circular plate of radius R. The moment of inertia of the remaining portion about an axis through O perpendicular to plane of the plate (i.e about the
axis
is ( M= mass of remaining circular plate. )
![](data:image/png;base64,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)
A circular plate of radius 1/2R is cut from one edge of a thin circular plate of radius R. The moment of inertia of the remaining portion about an axis through O perpendicular to plane of the plate (i.e about the
axis
is ( M= mass of remaining circular plate. )
![](data:image/png;base64,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)
physics-General
physics-
A symmetrical lamina of mass M consists of a square shape with a semicircular section over each of the edge of the square as shown. The moment of inertia of the lamina about an axis through the centre of mass and perpendicular to the plane is
. The moment of inertia about the tangent
in the plane of the lamina is
![](data:image/png;base64,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)
A symmetrical lamina of mass M consists of a square shape with a semicircular section over each of the edge of the square as shown. The moment of inertia of the lamina about an axis through the centre of mass and perpendicular to the plane is
. The moment of inertia about the tangent
in the plane of the lamina is
![](data:image/png;base64,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)
physics-General
physics-
A uniform disc of radius R lies in x-y plane with its centre at origin. Its moment of inertia about the axis x= 2R and y=0 is equal to the moment of inertia about the axis y=d and z=0. Where d is equal to
![](data:image/png;base64,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)
A uniform disc of radius R lies in x-y plane with its centre at origin. Its moment of inertia about the axis x= 2R and y=0 is equal to the moment of inertia about the axis y=d and z=0. Where d is equal to
![](data:image/png;base64,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)
physics-General