Question

A cylinder rolls on the planks $A$ and $B$ without relative sliding. If the planks move with velocities $-2v\hat{i},v\hat{i}$ respectively and the plank $A$ has acceleration $\overrightarrow{a}(a=a\hat{i})$, find the : (a) $v_C$ and $v_Q$ and (b) $a_C$ and $a_Q$. Then

• A. $v_c=-\frac{v}{2}\hat{i}$ and $v_Q=-\frac{3}{2}v\hat{j}-\frac{v}{2}\hat{i}$
  
• B. $v_c=-\frac{v}{4}\hat{i}$ and $v_Q=-\frac{3}{4}v\hat{j}-\frac{v}{2}\hat{i}$
• C. $a_c=\frac{a}{2}\hat{i}$ and $a_Q=\left(\frac{9v^2}{4R}\right)\hat{i}+\frac{a}{2}\hat{j}$.
• D. $a_c=\frac{a}{4}\hat{i}$ and $a_Q=\left(\frac{9v^2}{16R}\right)\hat{i}+\frac{a}{2}\hat{j}$.

Answer 1

Answer: (A), (C)

The correct options are
A

$v_c=-\frac{v}{2}\hat{i}$ and $v_Q=-\frac{3}{2}v\hat{j}-\frac{v}{2}\hat{i}$

C $a_c=\frac{a}{2}\hat{i}$ and $a_Q=\left(\frac{9v^2}{4R}\right)\hat{i}+\frac{a}{2}\hat{j}$.