Question

Two weights $w_1$ and $w_2$ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up at an acceleration g, what will be the tension in the string?

Answer 1

We know weight= mass$\times$gravity;thus weight pf object 1$=\frac{Mass\left(M_1\right)}{Gravity\left(g\right)}$ and

weight of object 2 =$=\frac{Mass\left(M_2\right)}{Gravity\left(g\right)}$

$M_{2}g-T=M_{2}a-g$--------(A)

$-M_{1}g+T=M_{1}a-g$-------(B)

(A)- (B)

$2M_{2}g-2M_{1}g=M_{2}a+M_{1}aa=\frac{2g(M_2-M_1)}{(M_1+M_2)}$-------(C)

Now tension in string is

T${=M}_{1}g+M_{1}a+M_{1}g=2M_{1}g+M_{1}a$

Reducing the value of mass of obejtc 1 we get,

$=\frac{W_1}{g}\{2g+\frac{2g(M_2-M_1)}{(M_1+M_2)}\}=W_1\left\{\frac{2(M_2+M_1)+2(M_2-M_1)}{(M_1+M_1)}\right\}=W_1\left\{\frac{4\frac{W_2}{g}}{\frac{W_1}{g}+\frac{W_2}{g}}\right\}=\frac{4W_1{W}_2}{W_1+W_2}$