Question

If pulleys shown in the diagram are smooth and massless and $a_1$ and $a_2$ are acceleration of blocks of mass $4kg$ and $8kg$ respectively, then

• A. $a_1=a_2$
• B. $a_1=2a_2$
• C. $2a_1=a_2$
• D. $a_1=4a_2$

Answer 1

The correct option is B $a_1=2a_2$

$\begin{array}{c}\text{from the given picture, we devided the}\\ \text{parts of string in}{x}_1,x_2,x_3\\ \text{now,}\\ \text{as the string is constant}t\text{length}\\ x_1+x_2+x_3=c\end{array}$

$\begin{array}{c}\frac{d{x}_1}{dt}+\frac{d{x}_2}{dt}+\frac{d{x}_3}{dt}=0\\ \text{again differentiating}\\ \frac{d^2{x}_1}{d{t}^2}+\frac{d^2{x}_2}{d{t}^2}+\frac{d^3{x}_3}{d{t}^3}=0\end{array}$

$\begin{array}{c}\text{as,}{x}_1\text{increasing,}{x}_2\text{\&}{x}_3\text{decreasing}\\ \therefore a_1-a_2-a_2=0,\frac{d^2{x}_2}{d{t}^2}=\frac{3x_3}{d{t}^3}=a_2\\ \text{on}{a}_1=2a_2\end{array}$

Ans B