Question

If the block $\text{B}$ moves towards right with acceleration $\text{b}$, then the net acceleration of block $\text{A}$ is

• A. $b\hat{i}+4b\hat{j}$
• B. $b\hat{i}+b\hat{j}$
• C. $b\hat{i}+2b\hat{j}$
• D. None of these

Answer 1

The correct option is A $b\hat{i}+4b\hat{j}$

$\because$ Block A is inside B and accelaration of B in X-direction is $b$.
$\therefore$ acceleration of A in x - direction is also $b$.
$\overrightarrow{a_x}=b\hat{i}$
Let's assume the velocity of block B in x - direction in $v_b$. Then the velocity of block A in y - direction is $4v_b$ as shown in figure.



$\therefore$ acceleration of block A in y - direction is also 4 times the acceleration of block B in x - direction.
$\therefore \overrightarrow{a_y}=4b\hat{j}$
$\therefore$ Net accelration of block A,
$\overrightarrow{a}=\overrightarrow{a_x}+\overrightarrow{a_y}=b\hat{i}+4b\hat{j}$