Question

Assertion: The center of mass of uniform triangular lamina is its centroid.
Reason: Centroid is the symmetrical center of the triangular lamina.
A) Both assertion and reason are correct and reason is the correct explanation for assertion.
B) Both assertion and reason are correct but reason is not the correct explanation of the assertion.
C) Assertion is correct but Reason is not correct.
D) Assertion is incorrect but Reason is correct.

Answer 1

Hint: Just keep in mind that center of mass is the point relative to a body where the whole mass of an object is concentrated whereas centroid is geometrical interpretation which refers to the geometrical center of the object.

Complete answer:
Now, let us first know, what is the center of mass and centroid?
CENTER OF MASS: Center of mass of a body or a particle is defined as the point on at which whole of the mass of the body is concentrated.

CENTROID: Centroid is defined as the point in a triangle at which all the three medians of a triangle intersect. Thus, we can also say that the centroid of a point of intersection of all the three medians of a triangle.
Now, from above, we can say that the center of mass of a uniform body lies at the geometric center of the body whereas the centroid is the geometrical center of the triangular lamina. Therefore, the center of mass of a triangular lamina will lie at the centroid. Therefore, the assertion is correct. Reason statement is also correct and it explains the concept of assertion.

Therefore, option (A) is the correct option.

Additional Information
Let us know more about centroid.
We can calculate the centroid of a triangle using the given formula,
$C = [(\dfrac{{{x_1} + {x_2} + {x_3}}}{3}),(\dfrac{{{y_1} + {y_2} + {y_3}}}{3})]$
Where $C$ is the centroid of a triangle, ${x_1}$ , ${x_2}$, ${x_3}$ are the $x$-coordinates of vertices of a triangle and ${y_1}$, ${y_2}$, ${y_3}$ are the $y$-coordinates of a triangle.
So, we can say that the centroid formula is used to determine coordinates of a triangle.

Note: The median of a triangle is a line drawn from the center of any one side to the opposite vertex. Also, remember that the centroid of a triangle divides all the medians of a triangle in the $2:1$ ratio. Also, we can not only calculate the median of a triangle but we can also calculate the medians of a right-angled triangle and square by using suitable formula.