Question

A $20\text{kg}$ block is placed on top of $50\text{kg}$ block as shown in figure. A horizontal force $F$ acting on $A$ causes an acceleration of $3{\text{m/s}}^2$ to $A$ and $2{\text{m/s}}^2$ to $B$ as shown in figure. For this situation mark out the correct statement(s).

• A. The friction force between $A$ and $B$ is $40\text{N}$
• B. The net force acting on $A$ is $150\text{N}$
• C. The value of $F$ is $190\text{N}$
• D. The value of $F$ is $150\text{N}$

Answer 1

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

The correct options are
A The friction force between $A$ and $B$ is $40\text{N}$
B The net force acting on $A$ is $150\text{N}$
C The value of $F$ is $190\text{N}$

There is a relative motion between $A$ and $B$ since there accelerations are different.
For $A$,
Writing Newton's second law
$F_{\text{net}}=m_A{a}_A$
$F-f=m_A{a}_A=50\times 3=150\text{N}$

For $B_1$,
$f=m_B{a}_B=20\times 2=40\text{N}$

Net force on $A$ is $F-f=150\text{N}$
$\therefore F=150+40=190\text{N}$