As shown, two blocks with masses m and M ( M m ) are pushed by a force F in both Case I and Case II. The surface is horizontal and frictionless. Let R 1 be the magnitude of force that m exerts on

Question

As shown, two blocks with masses m and M ( $M > m$ ) are pushed by a force F in both Case I and Case II. The surface is horizontal and frictionless. Let $R_{1}$ be the magnitude of force that m exerts on M in case I and $R_{II}$ be the magnitude force that m exerts on M in case II. Which of the following statements is true?

TestHub · Accepted Answer

In both cases the two blocks move together with common acceleration

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

Case I (F applied to M, contact pushes m): the force that m exerts on M equals the contact force needed to accelerate m:

$R_{I} = ma = \frac{mF}{M + m}$

Case II (F applied to m, contact pushes M): the force that m exerts on M must accelerate the bigger block M:

$R_{II} = Ma = \frac{MF}{M + m}$

Since M > m, we get R_I < R_II.

Correct option: (B).

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