All STD 11 - System of particles and rotational motion questions
Newest firstShowing 251–300 of 369 questions
- 251. A piece of wood of mass \(0.03\, kg\) is dropped from the top of a \(100\, m\) height building. At the same time, a bullet of mass \(0.02\, kg\) is fired vertically upward, with a velocity \(100\, ms^{- 1}\), from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is ........ \(m\). \((g = 10\, ms^{-2})\) 2019 Hard
- 252. A piece of wood of mass \(0.03\, kg\) is dropped from the top of a \(100\, m\) height building. At the same time, a bullet of mass \(0.02\, kg\) is fired vertically upward, with a velocity \(100\, ms^{- 1}\), from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is ........ \(m\). \((g = 10\, ms^{-2})\) 2019 Hard
- 253. A rectangles solid box of length \(0.3\, m\) is held horizontally, with one of its sides on the edge of a platform of height \(5\,m\). When released, it slips off the table in a very short time \(= 0.01\, s\), remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:
2019 Hard - 254. A rectangles solid box of length \(0.3\, m\) is held horizontally, with one of its sides on the edge of a platform of height \(5\,m\). When released, it slips off the table in a very short time \(= 0.01\, s\), remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to: 2019 Hard
- 255. A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be
2019 Hard - 256. A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be 2019 Hard
- 257. A rod of length \(50\,cm\) is pivoted at one end. It is raised such that if makes an angle of \(30^o\) fro the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in \(rad\,s^{-1}\) ) will be \((g = 10\,ms^{-2})\)
2019 Medium - 258. A rod of length \(50\,cm\) is pivoted at one end. It is raised such that if makes an angle of \(30^o\) fro the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in \(rad\,s^{-1}\) ) will be \((g = 10\,ms^{-2})\) 2019 Medium
- 259. A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights \(h_{sph}\) and \(h_{cyl}\) on the incline. The radio \(\frac{{{h_{sph}}}}{{{h_{cyl}}}}\) is given by
2019 Hard - 260. A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights \(h_{sph}\) and \(h_{cyl}\) on the incline. The radio \(\frac{{{h_{sph}}}}{{{h_{cyl}}}}\) is given by 2019 Hard
- 261. A solid sphere of mass \(M\) and radius \(R\) is divided into two unequal parts. The first part has a mass of \(\frac {7M}{8}\) and is converted into a uniform disc of radius \(2R.\) The second part is converted into a uniform solid sphere. Let \(I_1\) be the moment of inertia of the disc about its axis and \(I_2\) be the moment of inertia of the new sphere about its axis. The ratio of \(I_1/I_2\) is given by 2019 Hard
- 262. A solid sphere of mass \(M\) and radius \(R\) is divided into two unequal parts. The first part has a mass of \(\frac {7M}{8}\) and is converted into a uniform disc of radius \(2R.\) The second part is converted into a uniform solid sphere. Let \(I_1\) be the moment of inertia of the disc about its axis and \(I_2\) be the moment of inertia of the new sphere about its axis. The ratio of \(I_1/I_2\) is given by 2019 Hard
- 263. A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of \(\theta ,\) where \(\theta \) is the angle by which it has rotated, is given as \(k\theta ^2.\) If its moment of inertia is \(I\) then the angular acceleration of the disc is 2019 Hard
- 264. A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of \(\theta ,\) where \(\theta \) is the angle by which it has rotated, is given as \(k\theta ^2.\) If its moment of inertia is \(I\) then the angular acceleration of the disc is 2019 Hard
- 265. A string is wound around a hollow cylinder of mass \(5\, kg\) and radius \(0.5\,m\). If the string is now pulled with a horizontal force of \(40\, N\), and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be ......... \(rad/s^2\) .(Neglect the mass and thickness of the string)
2019 Medium - 266. A string is wound around a hollow cylinder of mass \(5\, kg\) and radius \(0.5\,m\). If the string is now pulled with a horizontal force of \(40\, N\), and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be ......... \(rad/s^2\) .(Neglect the mass and thickness of the string) 2019 Medium
- 267. A thin disc of mass \(M\) and radius \(R\) has mass per unit area \(\sigma (r) = kr^2\) where \(r\) is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is 2019 Hard
- 268. A thin disc of mass \(M\) and radius \(R\) has mass per unit area \(\sigma (r) = kr^2\) where \(r\) is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is 2019 Hard
- 269. A thin smooth rod of length \(L\) and mass \(M\) is rotating freely with angular speed \({\omega _0}\) about an axis perpendicular to the rod and passing through its centre. Two beads of mass \(m\) and negligible size are at the centre of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod will be 2019 Hard
- 270. A thin smooth rod of length \(L\) and mass \(M\) is rotating freely with angular speed \({\omega _0}\) about an axis perpendicular to the rod and passing through its centre. Two beads of mass \(m\) and negligible size are at the centre of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod will be 2019 Hard
- 271. A uniform rectangular thin sheet \(ABCD\) of mass \(M\) has length \(a\) and breadth \(b\), as shown in the figure. If the shaded portion \(HBGO\) is cut off, the coordinates of the centre of mass of the remaining portion will be
2019 Hard - 272. A uniform rectangular thin sheet \(ABCD\) of mass \(M\) has length \(a\) and breadth \(b\), as shown in the figure. If the shaded portion \(HBGO\) is cut off, the coordinates of the centre of mass of the remaining portion will be 2019 Hard
- 273. An \(L-\) shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If \(AB = BC\), and the angle made by \(AB\) with downward vertical is \(\theta\) then
2019 Hard - 274. An \(L-\) shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If \(AB = BC\), and the angle made by \(AB\) with downward vertical is \(\theta\) then 2019 Hard
- 275. Four particles \(A, B, C\) and \(D\) with masses \(m_A=m, m_B=2m, m_C=3m\) and \(m_D=4m\) are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is
2019 Hard - 276. Four particles \(A, B, C\) and \(D\) with masses \(m_A=m, m_B=2m, m_C=3m\) and \(m_D=4m\) are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is 2019 Hard
- 277. in circular plate of mass \(M\) and radius \(R\) has its density varying as \(p\left( r \right) = {p_0}\,r\) with \(P_0\) as constant and \(r\) is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is \(I = aMR^2\) . The value of the coefficient \(a\) is 2019 Hard
- 278. in circular plate of mass \(M\) and radius \(R\) has its density varying as \(p\left( r \right) = {p_0}\,r\) with \(P_0\) as constant and \(r\) is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is \(I = aMR^2\) . The value of the coefficient \(a\) is 2019 Hard
- 279. Let the moment of inertia of a hollow cylinder of length \(30\, cm\) (inner radius \(10\, cm\) and outer radius \(20\, cm\)), about its axis be \(I\). The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also \(I\), is ......... \(cm\). 2019 Hard
- 280. Let the moment of inertia of a hollow cylinder of length \(30\, cm\) (inner radius \(10\, cm\) and outer radius \(20\, cm\)), about its axis be \(I\). The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also \(I\), is ......... \(cm\). 2019 Hard
- 281. Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\). 2019 Medium
- 282. Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\). 2019 Medium
- 283. The equilateral triangle \(ABC\) is cut from a thin solid sheet of wood. (See figure) \(D, E\) and \(F\) are the mid points of its sides as shown and \(G\) is the centre of the triangle. The moment of inertia of the triangle about an axis passing through \(G\) and perpendicular to the plane of the triangle is \(I_0.\) If the smaller triangle \(DEF\) is removed from \(ABC,\) the moment of inertia of the remaining figure about the same axis is \(I.\) Then
2019 Hard - 284. The equilateral triangle \(ABC\) is cut from a thin solid sheet of wood. (See figure) \(D, E\) and \(F\) are the mid points of its sides as shown and \(G\) is the centre of the triangle. The moment of inertia of the triangle about an axis passing through \(G\) and perpendicular to the plane of the triangle is \(I_0.\) If the smaller triangle \(DEF\) is removed from \(ABC,\) the moment of inertia of the remaining figure about the same axis is \(I.\) Then 2019 Hard
- 285. The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal place: \((i)\) a ring of radius \(R,\,(ii)\) a solid cylinder of radius \(\frac {R}{2}\) nd \((iii)\) a solid sphere of radius \(\frac {R}{4}.\) If, in each case, the speed of the center of mass at bottom of the incline is same, the ratio of the maximum heights they climb is 2019 Hard
- 286. The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal place: \((i)\) a ring of radius \(R,\,(ii)\) a solid cylinder of radius \(\frac {R}{2}\) nd \((iii)\) a solid sphere of radius \(\frac {R}{4}.\) If, in each case, the speed of the center of mass at bottom of the incline is same, the ratio of the maximum heights they climb is 2019 Hard
- 287. The magnitude of torque on a particle of mass \(1\,kg\) is \(2.5\, Nm\) about the origin. If the force acting on it is \(1\,N\), and the distance of the particle from the origin is \(5\,m\), the angle between the force and the position vector is (in radians) 2019 Medium
- 288. The magnitude of torque on a particle of mass \(1\,kg\) is \(2.5\, Nm\) about the origin. If the force acting on it is \(1\,N\), and the distance of the particle from the origin is \(5\,m\), the angle between the force and the position vector is (in radians) 2019 Medium
- 289. The position vector of the centre of mass \(\vec r\, cm\) of an asymmetric uniform bar of negligible area of cross-section as shown in figure is
2019 Medium - 290. The position vector of the centre of mass \(\vec r\, cm\) of an asymmetric uniform bar of negligible area of cross-section as shown in figure is 2019 Medium
- 291. The time dependence of the position of a particle of mass \(m = 2\) is given by \(\vec r\,(t)\, = \,2t\,\hat i\, - 3{t^2}\hat j\) Its angular momentum with respect to the origin at time \(t = 2\) is 2019 Hard
- 292. The time dependence of the position of a particle of mass \(m = 2\) is given by \(\vec r\,(t)\, = \,2t\,\hat i\, - 3{t^2}\hat j\) Its angular momentum with respect to the origin at time \(t = 2\) is 2019 Hard
- 293. Three particles of masses \(50\, g\), \(100\, g\) and \(150\, g\) are placed at the vertices of an equilateral triangle of side \(1\, m\) (as shown in the figure). The \((x, y)\) coordinates of the centre of mass will be
2019 Hard - 294. Three particles of masses \(50\, g\), \(100\, g\) and \(150\, g\) are placed at the vertices of an equilateral triangle of side \(1\, m\) (as shown in the figure). The \((x, y)\) coordinates of the centre of mass will be 2019 Hard
- 295. To mop-clean a floor, a cleaning machine presses a circular mop of radius \(R\) vertically down with a total force \(F\) and rotates it with a constant angular speed about its axis. If the force \(F\) is distributed uniformly over the mop and the floor is \(\mu \), the torque, applied by the machine on the mop is 2019 Hard
- 296. To mop-clean a floor, a cleaning machine presses a circular mop of radius \(R\) vertically down with a total force \(F\) and rotates it with a constant angular speed about its axis. If the force \(F\) is distributed uniformly over the mop and the floor is \(\mu \), the torque, applied by the machine on the mop is 2019 Hard
- 297. Two coaxial discs, having moments of inertia \(I_1\) and \(\frac{I_1}{2}\) are a rotating with respectively angular velocities \(\omega_1\) and \(\frac{\omega_1}{2}\), about their common axes. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If \(E_f\) and \(E_i\) are the final and initial total energies, then \((E_f -E_i)\) is 2019 Hard
- 298. Two coaxial discs, having moments of inertia \(I_1\) and \(\frac{I_1}{2}\) are a rotating with respectively angular velocities \(\omega_1\) and \(\frac{\omega_1}{2}\), about their common axes. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If \(E_f\) and \(E_i\) are the final and initial total energies, then \((E_f -E_i)\) is 2019 Hard
- 299. Two identical spherical balls of mass \(M\) and radius \(R\) each are stuck on two ends of a rod of length \(2R\) and mass \(M\) (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is
2019 Hard - 300. Two identical spherical balls of mass \(M\) and radius \(R\) each are stuck on two ends of a rod of length \(2R\) and mass \(M\) (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is 2019 Hard
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