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 1 and 2 respectively then,

• A. $A=(a_1+a_2)$
• B. $A=(a_1-a_2)$
• C. $A=\frac{a_1-a_2}{2}$
• D. $A=\frac{a_1+a_2}{2}$

Answer 1

Answer: (D)

Since length of the string is constant. So,

$(Y_p-y_1)+\pi R=\left(Y_p-y_2\right)$ = constant

Take derivative of both sides twice w.r.t. time t,

We get, $\stackrel{..}{Y_p}-\ddot{y_1}+0+\ddot{Y_p}-\ddot{Y_2}=0$

$2\ddot{Y_p}=\ddot{y_1}+\ddot{y_2}$

$\Rightarrow 2A=a_1+a_2$

$\Rightarrow A=\frac{a_1+a_2}{2}$