Question

The relation between the magnitudes of acceleration of pulley $P_1$ ($a_{p_1}$) and that of pulley $P_3$ ($a_{p_3}$) is

• A. $a_{p_1}$ = $2a_{p_3}$
• B. $a_{p_1}$ = $3a_{p_3}$
• C. $2_{p_1}$ = $a_{p_3}$
• D. $2a_{p_1}$ = $a_{p_3}$

Answer 1

The correct option is A

$a_{p_1}$ = $2a_{p_3}$

$\therefore$ $x_1$ + $x_1$ - $x_2$ + $x_3$ - $x_2$ + $x_3$ - $x_1$ = L

L is length of string.

$\Rightarrow$ $x_1$ - 2$x_2$ + 2$x_3$ = L

Assuming mass 'm' moves downward

$P_1$ will move up. Which means distance from $P_1$ and reference point will reduce.

$\therefore \frac{d^2{x}_1}{d{t}^2}=-a\left(p_1\right)$

Differentiating twice

$\therefore$ $\Rightarrow$ - $a_1$ - 0 + 2$a_3$ = 0 ($x_2$ is constant)

$\Rightarrow$ 2 $a_3$ = $a_1$

$\Rightarrow$ 2a($p_3$) = a($p_1$)