Question

In the given constraint, if the the surface and the pulley are frictionless and the string is inextensible, then velocity of the block $A$parallel to the smooth surface is

• A. $\frac{5}{\sqrt{3}}\text{m/s}$
• B. $3\text{m/s}$
• C. $5\text{m/s}$
• D. $10\text{m/s}$

Answer 1

The correct option is A $\frac{5}{\sqrt{3}}\text{m/s}$


For an inextensible string velocity component of the end points along the string will be same.
$\Rightarrow V_A\cos {30}^{\circ }=V_B\cos {60}^{\circ }$
$\Rightarrow V_A=5\times \frac{1}{2}\times \frac{2}{\sqrt{3}}$
$\Rightarrow V_A=\frac{5}{\sqrt{3}}\text{m/s}$