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, $T_2=\frac{\left(m_3+m_4\right)F}{m_1+m_2+m_3+m_4}$
$\Rightarrow T_2=\frac{1}{2}F$
$T_3=\frac{\left(m_4\right)F}{m_1+m_2+m_3+m_4}$
$\Rightarrow =\frac{1}{4}F$