Question

A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and the block is sliding radially outward on it with an uniform velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If OA = 1 m,, the magnitude of the absolute acceleration of the block at location A in m/s${}^2$ is

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is C 5

Acceleration of the block at
$A={\overrightarrow{a}}_{cr}+{\overrightarrow{a}}_r$

$=\overrightarrow{2\omega V}+\overrightarrow{{\omega }^{2}r}$

$\Rightarrow r=OA$

$\Rightarrow 2\omega V=2\times 2\times 0.75=3m/s^2$

$\Rightarrow$ ${\omega }^{2}r=2^2\times 1=4m/s^2$

Coriolis components and radial components are perpendicular to each other.

So, $|{\overrightarrow{a}}_{abc}|=\sqrt{3^2+4^2}=5m/s^2$