Three rods each of mass m and length b form an equilateral triangle and rotate about the median of the triangle. Its moment of inertia is (a m b2/16). Find a.

Question

Three rods each of mass m and length b form an equilateral triangle and rotate about the median of the triangle. Its moment of inertia is (a m b2/16). Find a. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

M.I. =2 (m b2/3) sin 2 30°+(m b2/12)=(m b2/6)+(m b2/12)=(m b2/4)

Q. Three rods each of mass $m$ and length $b$ form an equilateral triangle and rotate about the median of the triangle. Its moment of inertia is $\frac{am b ^{2}}{16}$ . Find $a$ .

$M . I . = 2 \frac{m b ^{2}}{3} sin^{2} 3 0^{\circ} + \frac{m b ^{2}}{12} = \frac{m b ^{2}}{6} + \frac{m b ^{2}}{12} = \frac{m b ^{2}}{4}$

Q. Three rods each of mass m and length b form an equilateral triangle and rotate about the median of the triangle. Its moment of inertia is 16amb2​. Find a.

M.I.=23mb2​sin230∘+12mb2​=6mb2​+12mb2​=4mb2​

Q. Three rods each of mass $m$ and length $b$ form an equilateral triangle and rotate about the median of the triangle. Its moment of inertia is $\frac{am b ^{2}}{16}$ . Find $a$ .

$M . I . = 2 \frac{m b ^{2}}{3} sin^{2} 3 0^{\circ} + \frac{m b ^{2}}{12} = \frac{m b ^{2}}{6} + \frac{m b ^{2}}{12} = \frac{m b ^{2}}{4}$