Three particles, each of mass m gram are situated at the vertices of an equilateral triangle ABC of side l cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-on2 units will be

Question

Three particles, each of mass m gram are situated at the vertices of an equilateral triangle ABC of side l cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-on2 units will be (A)  (3/4)ml2  (B)  2ml2  (C)  (5/4)ml2  (D)  (3/2)ml2

Tardigrade Admin · Accepted Answer

Moment of inertia c<the system about axis AX, =IA+IB+IC =mA(rA)2+mB(rB)2+mC(rC)2 =m(0)2+m(l)2+m(l cos 60)2 =ml2+(ml2/4)=(5ml2/4)

Q. Three particles, each of mass m gram are situated at the vertices of an equilateral triangle ABC of side $l$ cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-on2 units will be

$\frac{3}{4} m l^{2}$

$2 m l^{2}$

$\frac{5}{4} m l^{2}$

$\frac{3}{2} m l^{2}$

Moment of inertia c $A X, = I_{A} + I_{B} + I_{C} = m_{A} (r_{A})^{2} + m_{B} (r_{B})^{2} + m_{C} (r_{C})^{2} = m (0)^{2} + m (l)^{2} + m (l cos 60)^{2} = m l^{2} + \frac{m l ^{2}}{4} = \frac{5 m l ^{2}}{4}$

Q. Three particles, each of mass m gram are situated at the vertices of an equilateral triangle ABC of side l cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-on2 units will be

43​ml2

2ml2

45​ml2

23​ml2