The moment of inertia of a uniform sphere of radius r...

Home / Engineering Physics / Classical Mechanics / Question

Examveda

The moment of inertia of a uniform sphere of radius, r about an axis passing through its centre is given by $$\frac{2}{5}\left( {\frac{{4\pi }}{3}{r^5}\rho } \right).$$ A rigid sphere of uniform mass density $$\rho $$ and radius R has two smaller spheres of radii $$\frac{R}{2}$$ hollowed out of it as shown in the figure given below.

The moment of inertia of the resulting body about Y-axis is

A. $$\frac{{\pi \rho {R^5}}}{4}$$

B. $$\frac{{5\pi \rho {R^5}}}{{12}}$$

C. $$\frac{{7\pi \rho {R^5}}}{{12}}$$

D. $$\frac{{3\pi \rho {R^5}}}{4}$$

Answer: Option B

Related Questions on Classical Mechanics

A. increases till mass falls into hole

B. decreases till mass falls into hole

C. remains constant

D. becomes zero at radius r₁, where 0 < r₁ < r₀

View Answer

A. $$\frac{c}{3}$$

B. $$\frac{{\sqrt 2 }}{3}c$$

C. $$\frac{c}{2}$$

D. $$\frac{{\sqrt 3 }}{2}c$$

View Answer

A. $$\frac{{{p_x}^2}}{{2a}} + \frac{{{p_y}^2}}{{2b}} + kxy$$

B. $$\frac{{{p_x}^2}}{{4a}} + \frac{{{p_y}^2}}{{4b}} - kxy$$

C. $$\frac{{{p_x}^2}}{{4a}} + \frac{{{p_y}^2}}{{4b}} + kxy$$

D. $$\frac{{{p_x}^2 + {p_y}^2}}{{4ab}} + kxy$$

View Answer

A. circular

B. elliptical

C. parabolic

D. hyperbolic

View Answer