Question

Four blocks of same mass connected by cords are pulled by a force $F$ on a smooth horizontal surface, as shown in figure. The tensions $T_{1}$, $T_{2}$ and $T_{3}$ will be

• A. $T_{1}=\frac{1}{4}F, T_{2}=\frac{3}{2}F, T_{3}=\frac{1}{4}F$
• B. $T_{1}=\frac{1}{4}F, T_{2}=\frac{1}{2}F, T_{3}=\frac{1}{2}F$
• C. $T_{1}=\frac{3}{4}F, T_{2}=\frac{1}{2}F, T_{3}=\frac{1}{4}F$
• D. $T_{1}=\frac{3}{4}F, T_{2}=\frac{1}{2}F, T_{3}=\frac{1}{2}F$

Answer 1

Answer: (C)

$T_{1}=\frac{\left(m_{2}+m_{3}+m_{4}\right) F}{m_{1}+m_{2}+m_{3}+m_{4}}$

$\therefore T_{1}=\frac{3}{4} F$
Similarly, $T_{2} =\frac{\left(m_{3}+m_{4}\right) F}{m_{1}+m_{2}+m_{3}+m_{4}}$
$\Rightarrow T_{2} =\frac{1}{2} F$
$T_{3} =\frac{\left(m_{4}\right) F}{m_{1}+m_{2}+m_{3}+m_{4}}$
$\Rightarrow =\frac{1}{4} F$