Question

Assertion: Linear mass density has the dimensions of $[ M L^{1}T^{0}]$
Reason: Because density is always mass per unit volume.
a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
b) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c) Assertion is correct but Reason is incorrect.
d) Both Assertion and Reason are incorrect.

Answer 1

Hint: Linear mass density is the mass per length. The kilogram per meter is the SI unit of linear mass density. Linear density is the estimation of a quantity of any feature value per unit length. Linear mass density is the measure of mass per unit length. The linear mass density has an SI unit is the kilogram per meter. Many methods can measure the linear density of fibres and yarns.

Complete step-by-step solution:
Linear density is the estimation of a quantity of any particular value per unit of length. Linear mass density and linear charge density are two common examples utilized in science and engineering.
The term linear density is commonly used when describing one-dimensional objects' characteristics, although linear density can also define the density of a three-dimensional measure along one unique dimension. Just as density is most frequently used to determine mass density, the term linear density often leads to linear mass density. However, this is only one case of a linear density, as any amount can be estimated in terms of its amount along one dimension.
Consider a large, thin rod having mass m and length l. Its linear mass density:
$\lambda_{m} = \dfrac{m}{l}$
Dimension of mass is $[M]$.
Dimension of length is $[L]$.
Dimension of linear mass density is $\lambda_{m} = \dfrac{[M]}{[L]}$ i.e., $[M L^{-1}T^{0}]$.
Assertion and Reason both are wrong.
Option (d) is correct.

Note:Linear mass density is the measure of mass per unit length. Just as typical density is mass per unit volume, linear density is mass per unit length. Linear densities are generally used for large thin objects such as series for musical instruments. The linear density, represented along a single dimension.