Question

By what distance do the wedges move if 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 $x\cot \theta \text{cm}$

By the condition of wedge constrained, the accelerations along the normal to the common interface are equal.
Let the plank acceleration be $a_P$
and the wedges acceleration be $a_W$
$x\cos \theta =x_0\sin \theta$
($\because$ displacement will be in ratio of acceleration)
$x_0=x\cot \theta$