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In the figure shown mass of both, the spherical body and block is m. Moment of inertia of the spherical body about centre of mass is 2 mR^2 . The spherical body rolls on horizontal surface. There is no slipping at any surfaces in contact. The ratio of kinetic energy of the spherical body to that of block is
30
Sep
In the figure shown mass of both, the spherical body and block is m. Moment of inertia of the spherical body about centre of mass is 2 mR^2 . The spherical body rolls on horizontal surface. There is no slipping at any surfaces in contact. The ratio of kinetic energy of the spherical body to [...]
Two cylinders having radii 2R and R and moment of inertia 4I and I about their central axes are supported by axles perpendicular to their planes. The large cylinder is initially rotating clockwise with angular velocity ω0. The small cylinder is moved to the right until it touches the large cylinder and is caused to rotate by the frictional force between the two. Eventually slipping ceases and the two cylinders rotate at constant rates in opposite directions. During this
30
Sep
Two cylinders having radii 2R and R and moment of inertia 4I and I about their central axes are supported by axles perpendicular to their planes. The large cylinder is initially rotating clockwise with angular velocity ω0. The small cylinder is moved to the right until it touches the large cylinder and is caused to [...]
A mass m is moving at speed v perpendicular to a rod of length d and mass M = 6 m pivots around a frictionless axle running through its centre and stickes to the end of the rod. The moment of inertia od the rod about its centre is Md 2/12. Then the angular speed of the system right after the collision us –
30
Sep
A mass m is moving at speed v perpendicular to a rod of length d and mass M = 6 m pivots around a frictionless axle running through its centre and stickes to the end of the rod. The moment of inertia od the rod about its centre is Md 2/12. Then the angular speed [...]
A uniform rod of mass m and length l is placed over a smooth horizontal surface along the y-axis and is at rest as shown in figure an impulsive force F is applied for a small time Δt along x-direction 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)]
30
Sep
A uniform rod of mass m and length l is placed over a smooth horizontal surface along the y-axis and is at rest as shown in figure an impulsive force F is applied for a small time Δt along x-direction at point A. The x-coordinate of end A of the rod when the rod becomes [...]
In the figure shown, a ring A is initially rolling without sliding with a velocity 1, on the horizontal surface of the body B (of same mass as A). All surfaces arc smooth. B has no initial velocity. What will be the maximum height reached by A on B?
30
Sep
In the figure shown, a ring A is initially rolling without sliding with a velocity 1, on the horizontal surface of the body B (of same mass as A). All surfaces arc smooth. B has no initial velocity. What will be the maximum height reached by A on B? a ring A is initially rolling [...]
A thin uniform rod of mass m and length l is kept on a smooth horizontal surface such that it can move freely. At what distance from centre of rod should a particle of mass m strike on the rod such that the point P at a distance l3 from the end of the rod is instantaneously at rest just after the elastic collision?
30
Sep
A thin uniform rod of mass m and length l is kept on a smooth horizontal surface such that it can move freely. At what distance from centre of rod should a particle of mass m strike on the rod such that the point P at a distance l3 from the end of the rod [...]
A conical pendulum consists of a mass M suspended from a strong sling of length l. The mass executes a circle of radius R in a horizontal plane with speed v. At time t, the mass is at position R i ^ and has v j ^ velocity. At time t, the angular momentum vector of mass M about the point from which the string passes on the ceiling is
30
Sep
A conical pendulum consists of a mass M suspended from a strong sling of length l. The mass executes a circle of radius R in a horizontal plane with speed v. At time t, the mass is at position R i ^ and has v j ^ velocity. At time t, the angular momentum [...]
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A conical pendulum consists of a mass M suspended from a strong sling of length l. The mass executes a circle of radius R in a horizontal plane with speed v. At time t ,
the angular momentum vector of mass M about the point from which the string passes on the ceiling is ,
the mass is at position R i ^ and has v j ^ velocity. At time t ,
A solid sphere rests on a horizontal surface. A horizontal impulse is applied at height h from centre. The sphere starts rolling just after the application of impulse. The ratio h/r will be
30
Sep
A solid sphere rests on a horizontal surface. A horizontal impulse is applied at height h from centre. The sphere starts rolling just after the application of impulse. The ratio h/r will be A solid sphere rests on a horizontal surface. A horizontal impulse is applied at height h from centre. The sphere starts rolling [...]
Seven pulleys are connected with the help of three light strings as shown in Fig. 6.363. Consider P3, P4, P5 as light pulleys and pulleys P6 and P7 have masses m each. For this arrangement, mark the
29
Sep
Seven pulleys are connected with the help of three light strings as shown in Fig. 6.363. Consider P3, P4, P5 as light pulleys and pulleys P6 and P7 have masses m each. For this arrangement, mark the mark the P4 P5 as light pulleys and pulleys P6 and P7 have masses m each. For this [...]
A block of mass m is placed in contact with one end of a smooth tube of mass M. A horizontal force F acts on the tube in each case (1) and (2). Then,
29
Sep
A block of mass m is placed in contact with one end of a smooth tube of mass M. A horizontal force F acts on the tube in each case (1) and (2). Then, A block of mass m is placed in contact with one end of a smooth tuve of mass M. A horizontal [...]