Question

For given figure, $m_{A}$ is $30\, kg , m_{B}=m_{C}=5\, kg$, respectively. All contact surfaces are smooth $\left(g=10\, m / s ^{2}\right)$. Select the correct statement(s).

• A. Acceleration of block $A, B$ and $C$ are $1\, m / s ^{2}, 3\, m / s ^{2}$ and $5\, m / s ^{2}$ respectively
• B. Contact force between $B$ and ground is $350\, N$
• C. Tension in string is $30 \,N$
• D. Contact force between $B$ and $C$ is $15\, N$

Answer 1

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

$T=\left(m_{B}+m_{C}\right) a$
$T=10 a$ ...(i)
$T=m_{A} a=m_{A} A$
$T+m_{A}(A-a)$ ...(ii)
$T=30(A-a)$
$\Rightarrow N=m_{C} a$ ...(iii)
$m_{C} g-T=m_{C} A$
$50-T=5 A$ ...(iv)
$A+2 a=10$ and $10 a=30(A-a)$
$4 a=3 A$
$A+\frac{3 A}{2}=10$

$A=4, a=3, T=30\, N , N=15\, N$
Contact force between $B$ and ground is $380\, N$
$N_{G}=5 g+30 g+ T=380\, N$