Question

Consider three masses $A$, $B$ and $C$ as shown in the figure. Friction coefficient between all surfaces is $0.5$. Pulleys are smooth. ($m_A=1kg,m_B=1kg$.) Mass of $C$

• A. It is possible that both $A$ and $B$ remain at rest
• B. It is possible that both $A$ and $B$ accelerate.
• C. It is possible that $A$ acceleration but $B$ does not accelerate.
• D. If $B$ acceleration, then $A$ definitely acceleration.

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A It is possible that $A$ acceleration but $B$ does not accelerate.
B If $B$ acceleration, then $A$ definitely acceleration.
C It is possible that both $A$ and $B$ remain at rest
D It is possible that both $A$ and $B$ accelerate.

$f{l}_1=f{l}_2=0.5\times 1\times g=5N,T$ can have any value depending on mass of $C$.
a. If $2T<5N$, then none of them accelerates.
b. If $T>5N$, both accelerate.
c. If $2T>5N$, but $T<5N$, then $A$ accelerates, $B$ does not accelerates.
d. If $B$ accelerates, then $T>5N$, so $2T>5N$, hence $A$ also accelerates.