A 10-N force is applied to mass M.The same force is applied to mass 4M.The ratio of the acceleration of the smaller mass to the acceleration of the larger mass is
A)4 to 1
B)20 to 1
C)1 to 1
D)1 to 2
E)1 to 4

Question

Quizplus · Accepted Answer

According to Newton's second law of motion, the force applied on an object is proportional to its acceleration, with the constant of proportionality being the mass of the object. Mathematically, F=ma.
Here, the force applied is the same for both masses, and the acceleration of each mass is directly proportional to its mass. Thus, the acceleration of mass M is a and the acceleration of mass 4M is 1/4 of a.
Therefore, the ratio of acceleration of smaller mass to larger mass is a/(1/4a), which simplifies to 4:1. Hence, the correct answer is A) 4 to 1.

A 10-N Force Is Applied to Mass M