First slide

Constraints

Question

In the arrangement shown in the figure, the acceleration of the pulley is, (Ignore friction and mass of the pulley).

Moderate

A

F/4M
B

F/M
C

Zero
D

F/2M

Solution

Constraint equation

x_p + (x_p – x_M) = L = length of the string ⇒ 2x_p - x_M = L
differentiating twice with respect to time, we get 2a_p – a_M = 0
$\begin{array}{rcl} a_{p} & = & \frac{a_{M}}{2} \\ a_{M} & = & \frac{F}{2 M} \\ \Rightarrow & a_{p} = \frac{F}{4 M} \end{array}$

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