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A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be
27
Nov
A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be A ball rolls without slipping. The radius of gyration of the ball [...]
A string of negligible thickness is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance l from the cylinder holds one end of the sitting an pulls the cylinder towards him figure. There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hands is
27
Nov
A string of negligible thickness is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance l from the cylinder holds one end of the sitting an pulls the cylinder towards him figure. There is no slipping anywhere. The length of the string passed through the hand [...]
A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then
27
Nov
A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then A is the point of contact A sphere is rolling without slipping on a fixed horizontal plane surface. In the [...]
A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane with speed 2v and v, respectively, strike the bar [as shown in the fig.] and stick to the bar after collision. Denoting angular velocity (about the centre of mass), total energy and centre of mass velocity by ω, E and vc respectively, we have after collision
27
Nov
A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane with speed 2v and v, respectively, strike the bar [as shown in the fig.] and stick to the bar after collision. Denoting angular velocity (about the centre of [...]
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A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane with speed 2v and v ,
E and vc respectively ,
respectively ,
strike the bar [as shown in the fig.] and stick to the bar after collision. Denoting angular velocity (about the centre of mass) ,
total energy and centre of mass velocity by ω ,
we have after collision ,
A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now the platform is given an angular velocity ω0 When the tortoise move along a chord of the platform with a constant velocity (with respect to the platform). The angular velocity of the platform ω(t) will vary with time t as
27
Nov
A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now the platform is given an angular velocity ω0 When the tortoise move along a chord of the platform with a constant velocity (with respect to [...]
A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following with not be affected ?
27
Nov
A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following with not be affected ? A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following with not [...]
A small particle of mass m is projected at an angle q with the x-axis with an initial velocity v0 in the x−y plane as shown in the figure. At a time t< v0 sinθ/g, the angular momentum of the particle is where i^,j^ and k^ are unit vectors along x,y and z−axis respectively.
27
Nov
A small particle of mass m is projected at an angle q with the x-axis with an initial velocity v0 in the x−y plane as shown in the figure. At a time t< v0 sinθ/g, the angular momentum of the particle is where i^,j^ and k^ are unit vectors along x,y and z−axis respectively. A [...]
he line of action of the resultant of two like parallel forces shifts by one-third of the distance between the forces when the two forces are interchanged. The ratio of the two forces is
27
Nov
he line of action of the resultant of two like parallel forces shifts by one-third of the distance between the forces when the two forces are interchanged. The ratio of the two forces is he line of action of the resultant of two like parallel forces shifts by one-third of the distance between the forces [...]
The density of a rod gradually decreases from one end to the other. It is pivoted at an end so that it can move about a vertical axis through the pivot. A horizontal force F is applied on the free end in a direction perpendicular to the rod. The quantities, that do not depend on which end of the rod is pivoted, are :
27
Nov
The density of a rod gradually decreases from one end to the other. It is pivoted at an end so that it can move about a vertical axis through the pivot. A horizontal force F is applied on the free end in a direction perpendicular to the rod. The quantities, that do not depend on [...]
The moment of inertia of a body about a given axis is 1.2 kg m^2 . Initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rad/s^2 must be applied about that axis for a duration of
27
Nov
The moment of inertia of a body about a given axis is 1.2 kg m^2 . Initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rad/s^2 must be applied about that axis for a duration of an angular acceleration of 25 rad/s^2 [...]