Question

Two fixed frictionless inclined planes making an angle $30^o$ and $60^o$ with the vertical are shown in figure two blocks $A$ and $B$ are placed on the two planes. What is the relative acceleration of $A$ with respect to $B$ ?

• A. Zero
• B. $4.9m{s}^{-2}$ in the vertical direction
• C. $4.9m{s}^{-2}$ in horizontal direction
• D. $9.8m{s}^{-2}$ in the vertical direction

Answer 1

Answer: (B)

${\overrightarrow{a}}_A=gsin60^{o}cos60\hat{i}$
$=\frac{g\sqrt{3}}{4}\hat{i}-\frac{3g}{4}\hat{j}$
${\overrightarrow{a}}_B=gsin30cos30\hat{i}-gsi{n}^2\hat{j}$
$=g\frac{3}{4}\hat{i}-\frac{g\hat{j}}{4}$
${\overrightarrow{a}}_{\frac{A}{B}}={\overrightarrow{a}}_{\frac{A}{B}}={\overrightarrow{a}}_A-{\overrightarrow{a}}_B$
$=\frac{-3g}{4}\hat{j}+\frac{g}{4}\hat{j}$
$=-29\hat{j}$
${\overrightarrow{a}}_{\frac{A}{B}}=-4.9\hat{j}$