A wheel of radius r is rolling on a straight | vedclass

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Question

(D) For a wheel rolling without slipping,the velocity of any point $P$ at a distance $r'$ from the point of contact $M$ is given by $v_P = \omega \cdo

Vedclass · Accepted Answer

The velocities of any two parts of the wheel which are equidistant from the centre are equal.

Vedclass · Answer

(D) For a wheel rolling without slipping,the velocity of any point $P$ at a distance $r'$ from the point of contact $M$ is given by $v_P = \omega \cdot MP$,where $\omega = v/r$. Thus,the velocity is proportional to $MP$. This makes statement $A$ correct.The point of contact $M$ has a velocity of $0$ relative to the ground,so it is instantaneously at rest. This makes statement $C$ correct.The velocity of a point at distance $d$ from the centre is $v_d = \sqrt{v^2 + (\omega d)^2 + 2v\omega d \cos 	heta}$. Since this depends on the angle $	heta$ relative to the vertical,points equidistant from the centre do not necessarily have the same velocity. Thus,statement $D$ is incorrect.Regarding statement $B$,the points with velocity greater than $v$ are those in the upper half of the wheel,and those with velocity less than $v$ are in the lower half. Since the velocity increases as we move from $M$ to $N$,the distribution is such that statement $B$ is considered correct in the context of rolling motion dynamics.

$A$ wheel of radius $r$ is rolling on a straight line,with the velocity of its centre being $v$. At a certain instant,the point of contact of the wheel with the ground is $M$ and $N$ is the highest point on the wheel (diametrically opposite to $M$). Which of the following statements is incorrect?

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