Question

At a certain moment of time, velocities of block 1 and 2 both are 1 $m/s$ upwards. Find the speed of block 3 at that moment. Assume that the strings are inextensible and pulley is frictionless.

• A. $1m/s$
• B. $2m/s$
• C. $3m/s$
• D. $5m/s$

Answer 1

The correct option is C $3m/s$


$x_1\text{and}{x}_p$ are the intercepts of the same string, so
$x_1+x_p=\text{constant}$ . . . . (i)
Similarly, $(x_2-x_P)+(x_3-x_p)=\text{constant}$ . . (ii)
Differentiating (i) & (ii) w.r.t. time $t$, we get
$V_1+V_P=0$ . . . . (iii)
and $V_2-V_P+V_3-V_P=0$
$\Rightarrow V_2+V_3-2V_P=0$ . . . . (iv)
Using (iii) and (iv), we get
$V_2+V_3+2V_1=0$
Taking, upward direction as positive we are given,
$V_1=V_2=1m/s$
$\therefore V_3=-3m/s$
i.e. velocity of block 3 is 3 $m/s$ (downwards).