Question

The speed of block $B$ in a pulley-block system as shown in figure is

• A. $5m/s$
• B. $6.5m/s$
• C. $7.5m/s$
• D. $10m/s$

Answer 1

The correct option is C $7.5m/s$

As the string is inextensible, components of the velocities of the bodies along the string should be equal otherwise, it will break.

So, velocities of the blocks along the string are given as
For block $A$, velocity is $V_A\cos {53}^{\circ }=10\cos {53}^{\circ }$.......(i)
For block $B$, velocity is $V_B\cos {37}^{\circ }$.....(ii)
So, from (i) & (ii), we have
$V_B\cos {37}^{\circ }=10\cos {53}^{\circ }$
$\Rightarrow V_B=\frac{10\times 3/5}{4/5}=\frac{30}{4}=\frac{15}{2}=7.5m/s$

$\therefore \cos {37}^{\circ }=\frac{4}{5},\cos {53}^{\circ }=\frac{3}{5}$