Question

A rod $\text{AB}$ is shown in figure. End $\text{A}$ of the rod is hinged on the ground. Block is moving with velocity $2\text{m/s}$ towards right. The velocity of end $\text{B}$ of rod at the instant shown in figure is

• A. $\sqrt{3}\text{m/s}$
  
• B. $2\text{m/s}$
• C. $2\sqrt{3}\text{m/s}$
• D. $4\text{m/s}$

Answer 1

The correct option is D $4\text{m/s}$

As rod is hinged at point $\text{A}$, it will rotate about point $\text{A}$, if block is displaced.
Suppose, tangential velocity of end $\text{B}$ is $V$ as shown in figure.

We know that, point contact of two surfaces have same velocity if they move together.
So, point of rod connected with block will have same velocity in the given direction.


Equating the velocity of point of contact along the horizontal direction, we get

$V\cos {60}^o=2$

$\Rightarrow V\times \frac{1}{2}=2$

$\therefore V=4\text{m/s}$

Why this question ? This question is application of the concept of velocity of contact points. Velocity of the points in contact are always same for two different bodies, when there is no relative slipping. As rod is hinged, it will rotate about the hinge point and it will have only tangential velocity.