Question

A wheel is rolling on a horizontal plane. At a certain instant, it has a velocity '$v$' and acceleration '$a$' of CM as shown in figure. Acceleration of:

• A. A is vertically upwards
• B. B may be vertically downwards
• C. C cannot be horizontal
• D. some point on the rim may be horizontal leftwards

Answer 1

Answer: (A), (B), (C)

C cannot be horizontal
A is vertically upwards
B may be vertically downwards

$\overrightarrow{a_{A/COM}}=-\alpha R\hat{i}+\frac{v^2}{R}\hat{j}\overrightarrow{a_{COM}}=\alpha R\hat{i}\overrightarrow{a_A}=\overrightarrow{a_{A/COM}}+\overrightarrow{a_{COM}}=\frac{v^2}{R}\hat{j}\overrightarrow{a_{B/COM}}=-\frac{v^2}{R}\hat{i}-\alpha R\hat{j}\overrightarrow{a_B}=\overrightarrow{a_{B/COM}}+\overrightarrow{a_{COM}}=(-\frac{v^2}{R}+\alpha R)\hat{i}-\alpha R\hat{j}whichisverticallydownwardsif-\frac{v^2}{R}+\alpha R=0\overrightarrow{a_{C/COM}}=\alpha R\hat{i}-\frac{v^2}{R}\hat{j}\overrightarrow{a_C}=\overrightarrow{a_{C/COM}}+\overrightarrow{a_{COM}}=2\alpha R\hat{i}-\frac{v^2}{R}\hat{j}anditca{n}^{\prime }tbehorizontal$