Question

Find the velocity of block $A$ i.e. $V_A$ and velocity of block $C$ i.e. $V_C$ respectively in the shown figure.

• A. $V_A=2\text{m/s}$, upwards and $V_C=17\text{m/s}$, downwards.
• B. $V_A=3\text{m/s}$, upwards and $V_C=20\text{m/s}$, upwards.
• C. $V_A=2\text{m/s}$, upwards and $V_C=17\text{m/s}$, upwards.
• D. $V_A=4\text{m/s}$, upwards and $V_C=22\text{m/s}$, downwards.

Answer 1

The correct option is C $V_A=2\text{m/s}$, upwards and $V_C=17\text{m/s}$, upwards.

Let us assume the block $A$ moves upwards and block $C$ moves downwards, and taking upward as positive we have

For pulley $P_2:$
$V_{P2}=\frac{V_B+V_A}{2}\Rightarrow 3=\frac{4+V_A}{2}\Rightarrow V_A=2\text{m/s}$
Similarly, for pulley $P_1:$
$V_{P1}=\frac{V_C+V_{P2}}{2}\Rightarrow 10=\frac{-V_C+3}{2}\Rightarrow V_C=-17\text{m/s}$
Hence, the velocity of block $A$ is $V_A=2\text{m/s}$, upwards and that of block $B$ is $V_C=17\text{m/s}$, upwards.