Question

Figure shows a uniform rod of length $30cm$ having mass of $30kg$. The strings shown in the figure are pulled by constant forces of $20N$ and $32N$. Find the force exerted by the $20cm$ part of the rod on the $10cm$ part. All the surfaces are smooth and the strings and the pulley are light

• A. $20N$
• B. $24N$
• C. $22N$
• D. $26N$

Answer 1

The correct option is B $24N$

Mass per unit length$=\frac{3}{30}$kg/cm$=0.1$kg/cm

Mass of $10$cm part$=m_1=1$kg

Mass of $20$cm part$=m_2=2$kg

Let $F$ be the force of contact between them

From free body diagram,

$F-20-a=0$ ......$\left(1\right)$

$32-F-2a=0$ ......$\left(2\right)$

$\Rightarrow 32-20-2a-a=0$

$\Rightarrow 12-3a=0$

$\Rightarrow a=\frac{12}{3}=4{ms}^{-2}$

Contact force$F=20+a=20+4=24$N

$\therefore$ force exerted$=24$N