Question

The ratio of the radii of gyration of a circular disc and a circular ring of the same radius about a tangential axis in the plane is ______.

विकल्प

• `sqrt3:sqrt4`

• `sqrt5:sqrt6`

• `sqrt6:sqrt5`

• `sqrt4:sqrt3`

Answer 1

The ratio of the radii of gyration of a circular disc and a circular ring of the same radius about a tangential axis in the plane is `bbunderline(sqrt5:sqrt6)`.

Explanation:

for disc `"mK"_alpha^2=5/4"mR"^2`

⇒ `"K"_alpha=sqrt5/2`R

for ring `"mK"_"r"^2=3/2"mR"^2`

⇒ `"K"_"r"=sqrt3/sqrt2`R

∴ `"K"_alpha/"K"_"r"=sqrt5/2xxsqrt2/sqrt3=sqrt5/sqrt6`