Question

Find the acceleration of the three masses $A,B$ and $C$ shown in figure. Friction coefficient between all surfaces is $0.5$. Pulleys are smooth. (Given $m_A=1kg,m_e=1kg,m{c}_o=2kg.)$

• A. $a_c=\frac{17g}{22}$
• B. $a_c=\frac{7g}{g}$
• C. $a_c=\frac{7g}{18}$
• D. $a_c=\frac{7g}{15}$

Answer 1

Answer: (A)

$a_c=\frac{17g}{22}$

correct option is (A)

Let acceleration of $c=a_c$

on $C\Rightarrow m_{e}g-T=m_e{a}_c---\left(1\right)$

on $A\Rightarrow 2T-\mu m_{A}g=m_A{a}_A--\left(2\right)$

on $B\Rightarrow T-\mu m_{B}g=m_B{a}_B-\dots -\left(3\right)$

By constraineds:

$2a_A+a_B=a_c-\dots -\left(4\right)$

putting all values

$\mu =1/2,m_A=m_c=1kg,m_B=2kg$

solving all equations; we get $a_c=\frac{17g}{22}$