An equilateral triangle ABC is cut from a thin solid sheet of wood, (see figure) D, E and F are the mid-points of its sides as shown and G is the center of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I₀. It the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. then :

(a)

I=I₀

(b)

I=I₀

(c)

I=

(d)

I=I₀

Question

Question ID - 50298 :-

An equilateral triangle ABC is cut from a thin solid sheet of wood, (see figure) D, E and F are the mid-points of its sides as shown and G is the center of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I₀. It the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. then :

(a)

I=I₀

(b)

I=I₀

(c)

I=

(d)

I=I₀

1 Answer

5876 Votes

score 3537 · Accepted Answer

Answer Key : (d) -

Suppose M is mass and a is side of larger triangle, then and will be mass and side length of smaller triangle

≈

=

So, I=I₀=

There are two long co-axial solenoids of same length l. the inner and outer coils have radii r₁ and r₂ and number of turns per unit length n₁ and n₂ respectively. The rate of mutual inductance to the self-inductance of the inner-coil is :
(a)		(b)
(c)		(d)