Question

A rod of length $l$ is in motion such that its ends $A$ and $B$ are moving along $x$ -axis and $y$ -axis respectively. It is giver that $\frac{d \theta}{d t}=2 \,rad / s$ always. $P$ is a fixed point on the rod. Let $M$ be the projection of $P$ on $x$ -axis. For the time interval in which $\theta$ changes from $0$ to $\frac{\pi}{2}$, choose the correct statement,

• A. The acceleration of $M$ is always directed towards right
• B. $M$ executes SHM
• C. $M$ moves with constant speed
• D. $M$ moves with constant acceleration

Answer 1

Answer: (B)

Given that $\frac{d \theta}{d t}=2 \,rad / s$
$\Rightarrow \theta=2 t$
Let $B P=a$
$\Rightarrow x=O M=a \sin \theta=a \sin (2 t)$

Hence $M$ executes SHM within the given time period and its acceleration is opposite to ' $x$ ' that means towards left.