Question

Weight W and 2W are supported in a vertical plane by a string and pulley as shown in figure. If we put an additional weight 'P' on the left side it will give a downward acceleration a = 0.2g to the weight W. What will be the value of P?

• A. 0.375W
• B. 0.75W
• C. 0.50W
• D. 0.25W

Answer 1

The correct option is A 0.375W


Initially when there is no additional weight P, then tension in all strings will be W.

$T_{string}=W$

Now, if acceleration of weight (W+P) is a downward; then acceleration of the weight 2W will be $\frac{a}{2}$ upward, Now tension in ropes will become T. Then
Now,
$(P+W)-T=\frac{(P+W)}{g}a=\frac{(P+W)\times 0.2g}{g}$

$(P+W)-T=0.2(P+W)$

T = 0.8 (P+W)

For pulley 2,

2T - 2W=$\left(\frac{2W}{g}\right)\left(\frac{a}{2}\right)$
$2\times 0.8(P+W)-2W=\frac{W\times 0.2g}{g}$

1.6P-0.4W = 0.2W

P = $\frac{0.6W}{1.6}=\frac{3}{8}W=0.375W$