Three point masses m1 , m2 ,m3 are located at the vertices of an equilateral triangle of length a. The moment of inertia of system about an axis along the altitude of the triangle passing through m1 is

Question

Three point masses m1 , m2 ,m3 are located at the vertices of an equilateral triangle of length a. The moment of inertia of system about an axis along the altitude of the triangle passing through m1 is (A) (m2 + m3) (a2/4) (B) (m2+m3)a2 (C) (m1+m2+m3)a2 (D) (m1+m2) (a2/2)

Tardigrade Admin · Accepted Answer

m1 becomes insignificant because it lies on the axis of rotation M.O.I = m2 ((a/2) )2 + m3 ( (a/2) )2 = (a2/4)(m2 + m3)

Q. Three point masses $m_{1}, m_{2}, m_{3}$ are located at the vertices of an equilateral triangle of length $a$ . The moment of inertia of system about an axis along the altitude of the triangle passing through $m_{1}$ is

$(m_{2} + m_{3}) \frac{a ^{2}}{4}$

$(m_{2} + m_{3}) a^{2}$

$(m_{1} + m_{2} + m_{3}) a^{2}$

$(m_{1} + m_{2}) \frac{a ^{2}}{2}$

$m_{1}$ becomes insignificant because it lies on the axis of rotation
M.O.I = $m_{2} (\frac{a}{2})^{2} + m_{3} (\frac{a}{2})^{2}$
= $\frac{a ^{2}}{4} (m_{2} + m_{3})$

Q. Three point masses m1​,m2​,m3​ are located at the vertices of an equilateral triangle of length a. The moment of inertia of system about an axis along the altitude of the triangle passing through m1​ is

(m2​+m3​)4a2​

(m2​+m3​)a2

(m1​+m2​+m3​)a2

(m1​+m2​)2a2​