Question

A 4 kg block A is placed on the top of a 8 kg block B which rests on a smooth table. A just slips on B when a force of 12 N is applied on A. Then the maximum horizontal force on B to make both A and B move together, is

• A. 12 N
• B. 24 N
• C. 36 N
• D. 48 N

Answer 1

Answer: (C)

36 N

Answer 2

Maximum friction i.e. limiting friction between A and B, $F_{l}$ = 12 N.

If F is the maximum value of force applied on lower body such that both body move together

It means Pseudo force on upper body is just equal to limiting friction

$F' = F_{l}$⇒ $m \left( \frac { F } { m + M } \right) =$ $\left( \frac{4}{4 + 8} \right)F = 12$ $\therefore F = 36N.$