91Ó°ÊÓ

• External force on the box-A, F = 100 N.
• Weight of box A = 150 N.
• Weight of box B = 50 N.

According to Newton's second law of motion, the force on a body is equal to its mass times acceleration.

The external force applied to the two-box system generates equal acceleration in the two boxes. If g is the acceleration due to gravity, the masses of the two boxes are,

$$\begin{gathered} m_A=\frac{150 N}{g} \\ {m}_B=\frac{50 N}{g} \end{gathered}$$

From the second law of motion, the acceleration a, produced in the boxes is,

$a=\frac{F}{M}$

Here M is the total mass on which F is acting.

Substitute the values in the above expression, and we get,

$$\begin{gathered} a=\frac{100N}{m_A+m_B} \\ =\frac{100N}{{\displaystyle \frac{150N}{g}}+{\displaystyle \frac{50N}{g}}} \\ =\frac{g}{2} \end{gathered}$$

The force exerted by box A on box B is$F_{AB}$then,

$$\begin{gathered} {\mathrm{F}}_{\mathrm{AB}}=\mathrm{a}×{\mathrm{m}}_{\mathrm{B}} \\ =\frac{\mathrm{g}}{2}×\frac{50\mathrm{N}}{\mathrm{g}} \\ =25\mathrm{N} \end{gathered}$$

Thus, the force exerted by box A on box B is 25 N which is much less than 100 N.