Question

The acceleration, a, of an object produced when a force is applied is given by the following formula, where F represents the force acting on the object and m represents the mass of the object.

a=F/m

If a has units of meters per second squared and m has units of grams, what must be the units of F?

A. grams
B. meters per second
C. grams·meters per second
D. grams·meters per second squared

Answer 1

Answer on Question #48709 – Physics – Mechanics | Kinematics | Dynamics

Question.

The acceleration, a, of an object produced when a force is applied is given by the following formula, where F represents the force acting on the object and m represents the mass of the object.

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

If a has units of meters per second squared and m has units of grams, what must be the units of F?

A. grams

B. meters per second

C. grams·meters per second

D. grams·meters per second squared

Solution.

$$a = \frac {F}{m} \rightarrow F = m a$$ $$[ m ] = [ g ]$$ $$[ a ] = \left[ \frac {m}{s ^ {2}} \right]$$

So,

$$[ F ] = [ m ] \cdot [ a ] = \left[ \frac {g \cdot m}{s ^ {2}} \right]$$

Thus, answer is D. grams·meters per second squared.

Answer.

D. grams·meters per second squared $\left[\frac{g\cdot m}{s^2}\right]$

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