Question

A $10\text{kg}$ block is placed on the top of a $40\text{kg}$ block as shown. A horizontal force $F$ acting on $B$ causes an acceleration of $2{\text{m/s}}^2$ to $B$. For this situation mark out the correct statement(s).

• A. The acceleration of A may also be $4{\text{m/s}}^2$.
• B. The acceleration of A must also be $2{\text{m/s}}^2$.
• C. The coefficient of friction between the blocks may be $0.2$.
• D. The coefficient of friction between the blocks must be $0.2$ only.

Answer 1

Answer: (B), (C)

The correct options are
B The acceleration of A must also be $2{\text{m/s}}^2$.
C The coefficient of friction between the blocks may be $0.2$.




Using FBD,
For $B$,
$F-f=40a_2$
$100-f=80$
$f=20$
For $A$,
$f=10a_1$
$20=10a_1$
$a_1=2$

So, acceleration of A must be $2{\text{m/s}}^2.$

We can see that, $a_1=a_2=2{\text{m/s}}^2$
This is possible only when A doesnot slip on B,
$\therefore f\le f_L\Rightarrow 20\le \mu m_{A}g$
$\Rightarrow 20\le \mu \times 10g\Rightarrow \mu \ge 0.2$
Hence $\mu$ can be greater or equal to 0.2