The moment of inertia of a planar disc about a diameter is 8kgm2. What is the moment of inertia about an axis passing through its centre and perpendicular to the plane of disc?

Consider two perpendicular axis in the plane of a planar body, such that I1 = 2 I2. The moment of inertia about an axis perpendicular to the plane and passing through intersection of I1 & I2 is 9kgm2. Find the value of I1& I2.

A

I1 = 9kg m2, I2 = 4.5kgm2

B

I1 = 3kg m2, I2 = 6kg m2

C

I1 = 6kg m2, I2 = 3kg m2

D

I1 = 18kg m2, I2 = 9kg m2

According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $${I_{\text{P}}}$$) is given by (where, A = Area of the section, $${I_{\text{G}}}$$ = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)

A

$${I_{\text{P}}} = {I_{\text{G}}} + {\text{A}}{{\text{h}}^2}$$

B

$${I_{\text{P}}} = {I_{\text{G}}} - {\text{A}}{{\text{h}}^2}$$

C

$${I_{\text{P}}} = \frac{{{I_{\text{G}}}}}{{{\text{A}}{{\text{h}}^2}}}$$

D

$${I_{\text{P}}} = \frac{{{\text{A}}{{\text{h}}^2}}}{{{I_{\text{G}}}}}$$

Three consecutive absorption lines at 64.275 cm^-1, 77.130 cm^-12 and 89.985 cm^-1 have been observed in a microwave spectrum for a linear rigid diatomic molecule. The moments of inertia $${I_A}$$ and $${I_B}$$ are ($${I_A}$$ is with respect to the bond axis passing through the centre of mass and $${I_B}$$ is with respect to an axis passing through the centre of mass and perpendicular to bond axis)

A

both equal to $$\frac{{{\hbar ^2}}}{{12.855\,hc}}$$ g-cm2

B

zero and $$\frac{{{\hbar ^2}}}{{12.855\,hc}}$$ g-cm2

C

both equal to $$\frac{{{\hbar ^2}}}{{6.427\,hc}}$$ g-cm2

D

zero and $$\frac{{{\hbar ^2}}}{{6.427\,hc}}$$ g-cm2

The moment of inertia of a ring about a tangent is 4kgm2. What is the moment of inertia about an axis passing through the centre of the ring and perpendicular to its plane? Mass of the ring is 2kg & diameter is 2m.

A

2kgm2

B

4kgm2

C

8kgm2

D

1kgm2

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

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

The moment of inertia of a uniform circular disc about its diameter is 100 gcm2. What is its moment of inertia about an axis perpendicular to its plane.

A

500 gcm2

B

100 gcm2

C

200 gcm2

D

700 gcm2

A rectangle is having base b and height h. The ratio of the moment of inertia when axis is passing through its base to moment of inertia of when axis passing through center of gravity and parallel to base is ___________

A

3

B

4

C

12

D

9

A triangle is having base b and height h. The ratio of the moment of inertia when axis is passing through its base to moment of inertia of when axis passing through centroid and parallel to base is ______

A

3

B

6

C

12

D

9

The moment of inertia of a circular lamina of diameter ‘d’, about an axis perpendicular to the plane of the lamina and passing through its centre, is

A

$$\frac{{\pi {{\text{d}}^4}}}{{12}}$$

B

$$\frac{{\pi {{\text{d}}^4}}}{{16}}$$

C

$$\frac{{\pi {{\text{d}}^4}}}{{24}}$$

D

$$\frac{{\pi {{\text{d}}^4}}}{{32}}$$

E

$$\frac{{\pi {{\text{d}}^4}}}{{36}}$$

A spherical body is symmetrical about its perpendicular axis. According to Routh's rule, the moment of inertia of a body about an axis passing through its centre of gravity is (where, M = Mass of the body and S = Sum of the squares of the two semi-axes.)

A

$$\frac{{{\text{MS}}}}{3}$$

B

$$\frac{{{\text{MS}}}}{4}$$

C

$$\frac{{{\text{MS}}}}{5}$$

D

None of these