Question

Figure shows a uniform rod of length $30 \,cm$ having a mass of $3.0 \,kg$. The strings shown in the figure are pulled by constant forces of $20 \,N$ and $32 \,N$. Find the force exerted by $20 \,cm$ part of the rod on the $10\, cm$ pan. All the surfaces are smooth and the strings and pulleys are light

• A. 36 N
• B. 12 N
• C. 64 N
• D. 24 N

Answer 1

Answer: (D)

Net force on the rod, $f=32-20=12\, N$
Acceleration of rod $=\frac{f}{m}=\frac{12}{3}=4 \,ms ^{-2}$
Equation of motion of $10\, cm$ part is
$F-20 =m \times a=1 \times 4 $
$F =4+20=24\, N$
Similarly, Equation of motion $20 \,cm$ part is
$32-F =m' a=2 \times 4 $
$F =32-8=24 \,N$