Question

Four rods each of length l have been hinged to form a rhombus. Vertex A is fixed to rigid support, vertex C is being moved along the x-axis with a constant velocity v as shown in the figure. The rate at which vertex B is approaching the x-axis at the moment the rhombus is in the form of a square is –

• A. $\frac { \mathrm { v } } { 4 }$
• B. $\frac { v } { 3 }$
• C. $\frac { v } { 2 }$
• D. $\frac { \mathrm { v } } { \sqrt { 2 } }$

Answer 1

Answer: (C)

$\frac { v } { 2 }$

Answer 2

Let AC = x and

BE = y

Then, BE² + AE² = l²

or y² + $\left( \frac { \mathrm { x } } { 2 } \right) ^ { 2 }$ = l²

\ 2y $\left( \frac { d y } { d t } \right)$ + $\frac { x } { 2 }$ . $\frac { \mathrm { dx } } { \mathrm { dt } }$ = 0

\ $\left( - \frac { d y } { d t } \right)$ = $\frac { 1 } { 2 }$ $\left( \frac { x } { 2 y } \right)$ . $\frac { \mathrm { dx } } { \mathrm { dt } }$

x = 2y, when the rhombus is a square.

Hence, v_B = $\frac { 1 } { 2 }$ v_c = $\frac { v } { 2 }$