Question

Two equal weight W and a single weight Q are attached to the ends, of a flexible but inextensible cord overhanging at a pulley as shown in figure, if the system moves with constant acceleration 'a'. What is the magnitude of the weight Q?

• A. $Q=\frac{2Wa}{g-a}$
• B. $Q=\frac{2\left(Wa\right)}{g-2a}$
• C. $Q=\frac{2Wg}{(g+a)}$
• D. $Q=\frac{2Wg}{(g-a)}$

Answer 1

The correct option is A

$Q=\frac{2Wa}{g-a}$

If T is the tension in cord.

Now,

$T-W=\frac{W}{g}a$

$(W+Q)-T=\left(\frac{W+Q}{8}\right)a$

$Q=\left(\frac{W+W+Q}{g}\right)a$

$Q-Q\left(\frac{a}{g}\right)=2W\left(\frac{a}{g}\right)$

$Q=\frac{2Wa\times g}{g\times (g-a)}=\frac{2Wa}{(g-a)}$