Which of the following statements are correct for instantaneous axis of rotation? 

a) 
Acceleration of every point lying on the axis be equal to zero 
b) 
Velocity of a point distance from the axis is equal to 
c) 
If moment of inertia of a body about the axis is and angular velocity is , then kinetic energy of the body is equal to 
d) 
Moment of inertia of a body is least about instantaneous axis of rotation among all the parallel axes 
Which of the following statements are correct for instantaneous axis of rotation? 

a) 
Acceleration of every point lying on the axis be equal to zero 
b) 
Velocity of a point distance from the axis is equal to 
c) 
If moment of inertia of a body about the axis is and angular velocity is , then kinetic energy of the body is equal to 
d) 
Moment of inertia of a body is least about instantaneous axis of rotation among all the parallel axes 
(b,c) In case of a wheel rolling on a horizontal plane, instantaneous axis of rotation of the wheel passes through (point of contact of wheel with plane). But at acceleration is vertically upwards. It means, acceleration at has nonzero value. Hence, option (a) is incorrect If the point is at a distance from the instantaneous axis of rotation, then its velocity (relative to the axis) will be equal to . But by definition, every point lying on the instantaneous axis of rotation is at rest at that instant. Therefore, the resultant velocity of the particle becomes equal to that relative velocity . Hence, option (b) is correct If distance of centre of mass of a body from the instantaneous axis of rotation is equal to and if its moment of inertia parallel to instantaneous axis of rotation but passing through centre of mass is equal to then Rotational KE of the body will be equal to and translation KE of the body will be , where . Therefore, translation KE becomes equal to . Hence, the total KE becomes equal to Hence, option (c) is correct In case of a wheel rotating on a plane, instantaneous axis of rotation of the wheel passes through which the centre of mass is at distance from In that case, the moment of inertia about instantaneous axis of rotation is equal to where is moment of inertia about the centroidal axis. Hence, moment of inertia of the wheel about the instantaneous axis of rotation is greater than the minimum possible value. Hence, option (d) is incorrect 
Write which number or alphabet in sequence replaces the question mark (?).
3, 14, 54, 159, 314, ? 

(a) 
309 
(b) 
372 
(c) 
391 
(d) 
398 
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