The linear density of a rope is the ratio of its mass per unit length. It is given by the equation λ=ml, where λ is the linear density, m is the mass, and l is the length. If the linear density of a rope is given with units of gcm and the distance is given in units of cm, what would be the units for mass?
a. g/cm
b.g times cm
c. g
d. 1/g
The answer is c. g.
is this the correct answer
Yes it is right
To determine the units of mass in the given equation λ = ml, we can analyze the units on both sides of the equation.
On the left-hand side, the linear density λ is given in grams per centimeter (g/cm), representing the mass per unit length. This indicates that the linear density has units of mass (grams) divided by length (centimeters).
On the right-hand side, m represents the mass of the rope. To find the units of m, we need to rearrange the equation:
λ = ml
Dividing both sides by l:
λ / l = m
Now, looking at the units:
(grams / centimeters) / centimeters = grams
Thus, the units for mass (m) are grams (g).