Question ID - 100701 | SaraNextGen Top Answer
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 If the point is at a distance If distance of centre of mass of a body from the instantaneous axis of rotation is equal to Rotational KE of the body will be 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 |
(point of contact of wheel with plane). But at 
acceleration is vertically upwards. It means, acceleration at 
has non-zero value. Hence, option (a) is incorrect
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
and if its moment of inertia parallel to instantaneous axis of rotation but passing through centre of mass is equal to 
then
and translation KE of the body will be 
, where 
. Therefore, translation KE becomes equal to 
. Hence, the total KE becomes equal to 
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 incorrectAnswer Link
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