Question

A block $A\left(5\text{kg}\right)$ rests over another block $B\left(3\text{kg}\right)$ placed over a smooth horizontal surface. There is friction between $A$ and $B$. A horizontal force $F_1$ gradually increasing from zero to a maximum is applied to $A$ so that the blocks move together without relative motion. Instead of this another horizontal force $F_2$, gradually increasing from zero to a maximum is applied to $B$ so that the blocks move together without relative motion. Then

• A. $F_1\text{(max)}=F_2\text{(max)}$
• B. $F_1\text{(max)}>F_2\text{(max)}$
• C. $F_1\text{(max)}<F_2\text{(max)}$
• D. $F_1\text{(max)}:F_2\text{(max)}=5:3$

Answer 1

Answer: (B), (D)

$F_1\text{(max)}:F_2\text{(max)}=5:3$

Case I:
Since, no relative motion, acceleration of both the blocks will be equal
$a=\frac{F_1-F_f}{5}=\frac{F_f}{3}\Rightarrow F_{1\text{(max)}}=\frac{8}{3}{F}_f$
Case II:
Again, since no relative motion, acceleration of both the blocks will be equal
$a=\frac{F_f}{5}=\frac{F_2-F_f}{3}\Rightarrow F_{2\text{(max)}}=\frac{8}{5}{F}_f$
Clearly;
$F_{1\text{(max)}}>F_{2\text{(max)}}$ and $\frac{F_{1\text{(max)}}}{F_{2\text{(max)}}}=\frac{5}{3}$