Which of the following statements is incorrect
(A) Torque is the rotational analogue of force
(B) Rolling motion of a cylinder down an inclined plane is combination of translational and rotational motion
(C) If the effort arm is larger than the load arm, the mechanical advantage is lesser than one
(D) For the extended body. centre of mass and centre of gravity do not coincide

Which among the following statements is/are incorrect? A. Friction acts against the direction of force. B. Motion can only be possible when driving force is more than friction. C. Ball thrown in the sky comes back to the ground due to gravity

Which of following statements are correct ? ltbgt (a) Centre of mass of a body always coincides with the centre of gravity of the body (b) Central of mass of a body is the point at which the total garvitational torque on the body is zero (c ) Couple on a body produces both trasnlational and rotation motion in a body (d) Mechinical advantage greater than one means that small efforts can be used to lift a large load

The following motion is based on the law of conservation of angular momentum (A) rotation of top (B) diving of driver (C) rotation of ballet dancer on smooth horizontal surface (D) a solid sphere that rolls down on an inclined plane

The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous exis passing through the centre of mass. These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless, stick as shown in the figure. When the disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed omega the motion at any instant can be taken as a combination of (i) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points P and Q). Both these motions have the same angular speed omega in this case Now consider two similar system as shown in the figure: Case (a) the disc with its face vertical and parallel to x-z plane, Case (b) the disc with its face making an angle of 45^@ with x-y plane and its horizontal diameter parallel to x-axis. In both the cases, the disc is welded at point P, and the systems are rotated with constant angular speed omega about the z-axis. Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?

A solid cylinder of mass 20 kg and radius 0.12 m rotating wit initial angula speed of 125 rad//s is placed lightly (i.e. without any translational push) on a horizontal table with coefficient of kinetic friction mu_(k) = 0.15 between the cylinder and the table. (a) After how long does the cylinder start rolling ? (b) What is the initial translational energy, rotational energy and total energy of the cylinder ? (c) What is the final (i.e. after rolling begins) translational energy, rotational energy and total energy of the cylinder ? (d) Is the finl total enrgy equal to the initial total energy of motion of the cylinder ? If not, where does the difference of energy disappear ? (e) Account for the loss of total energy of motion in the following way : find the work done by friction on the body its translational motion. Show that net work done by friction on the body is negative, equal in magnitude to the loss of total energy calculated in (d) above.

Read each statement below carefully and state with reasons, if it is true ot false. (a) During rolling the force of friction acts in the same direction as the direction of motion of c.m of the body. (b) The instantaneous speed of the point of contact during rolling is zero. (c ) The instantaneous acceleration of the point of contact during rolling is zero. (d) For perfect rolling motion, work done against friction is zero. (e) A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling motion).