Question

In the given constraint, what will be the speed of block $R$ $\left(V_R\right)$, if the string is inextensible and pulleys are frictionless?

• A. $10\text{m/s}$
• B. $12\text{m/s}$
• C. $14\text{m/s}$
• D. $16\text{m/s}$

Answer 1

The correct option is C $14\text{m/s}$


Since the string is inextensible, length of the string remains constant. $l_1$, $l_2$, $l_3$, $l_4$, and $l_5$ are the intercepts of the same string.
$\therefore l_1+l_2+l_3+l_4+l_5=\text{constant}$
Differentiating above equation to find rate of change of length which is velocity,
$V_B+V_C+V_F+V_G+V_R=0$
Here $V_B=V_C=V_P=5\text{m/s}$ and $V_F=V_G=V_Q=2\text{m/s}$
$\Rightarrow +5+5+2+2+V_R=0$
$\Rightarrow V_C=-14\text{m/s}$
($-ve$ sign indicates that $V_C$ should be upwards)