First slide

Constraints

Question

Two masses are connected by a string which passes over a pulley accelerating upward at a rate A shown. If $a_{1} and a_{2}$ be the accelerations of bodies I and 2 respectively then,

Moderate

A

$A = (a_{1} + a_{2})$
B

$A = (a_{1} - a_{2})$
C

$A = \frac{(a_{1} - a_{2})}{2}$
D

$A = \frac{a_{1} + a_{2}}{2}$

Solution

Since length of the string is constant. So,
$(Y_{P} - y_{1}) + πR + (Y_{p} - y_{2}) = constant . So,$
Take second derivative of both sides twice w.r.t. time t,
$W e g e t, (A - a_{1}) + 0 + [A - (- a_{2})] = 0 \Rightarrow A = \frac{a_{1} - a_{2}}{2}$

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