Question

By what distance do the wedges move, if the horizontal plank moves by $x\text{cm}$ downwards?

• A. $x\tan \theta \text{cm}$
• B. $x\cot \theta \text{cm}$
• C. $x\sin \theta \text{cm}$
• D. $x\cos \theta \text{cm}$

Answer 1

The correct option is B $x\cot \theta \text{cm}$

Both the wedges will move equal distance apart.
Let $x_0$ be the distance moved by the wedges as the plank moved $x\text{cm}$ downwards.
Also, let $v_0$ be the velocity of the wedges and $v$ be the velocity of the plank

So, from the condition of constraint, components of the velocity perpendicular to the point of contact at the surface should be equal.

$\therefore$ $v\cos \theta =v_0\sin \theta \Rightarrow v_0=v\cot \theta$
Or, in a given time displacements are equal.
$\Rightarrow x\cos \theta =x_0\sin \theta \Rightarrow x_0=x\cot \theta \text{cm}$