Moment of inertia of a system made from three uniform rods each of mass m and length l joined to each other, as shown in the figure about one end O and perpendicular to its plane will be

Option 1 - a

Option 2 - b

Option 3 - c

Option 4 - d

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Answered by

Raj Pandey | Contributor-Level 9

4 months ago

Correct Option - 4

Detailed Solution:

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Similar Questions for you

Two solid spheres each of mass 2 kg and radius 75 cm are arranged as shown. Find MOI of the system about the given axis.

Alok Kumar Singh

$I = (\frac{2}{5} M R^{2} + M R^{2}) \times 2$

$= \frac{14}{5} \times 2 \times \frac{9}{16}$

$= \frac{63}{20}$

= 3.15 kg m²

Alok Kumar Singh

Distance of CM from 5 kg = 10*2/15 = 4/3m

Two circular rings (of same material) are of same thickness. The diameter of first ring is twice that of second. The moment of inertia of first ring as compared to that of second is

Alok Kumar Singh

The momentum of inertia of a uniform thin rod about a perpendicular axis passing through on end is I1. The same rod is into a ring and its moment of inertia about a diameter is I2. If $\frac{I_{1}}{I_{2}} i s \frac{X π^{2}}{3},$ $\frac{_{}}{_{}} \frac{^{}}{}$ then the value of x will be__________.

Vishal Baghel

According to question, we can write

$l = 2 π r \Rightarrow r = \frac{l}{2 π}$

$I_{1} = \frac{m l^{2}}{3}, a n d I_{2} = \frac{m r^{2}}{2} = \frac{m l^{2}}{8 π^{2}}$

$\Rightarrow \frac{I_{1}}{I_{2}} = \frac{m l^{2}}{3} \times \frac{8 π^{2}}{m l^{2}} = \frac{8 π^{2}}{3}$

The momentum of inertia of a uniform thin rod about a perpendicular axis passing through on end is I₁. The same rod is into a ring and its moment of inertia about a diameter is I₂. If $\frac{I_{1}}{I_{2}} i s \frac{X π^{2}}{3},$ then the value of x will be__________.

Alok Kumar Singh

According to question, we can write

$l = 2 π r \Rightarrow r = \frac{l}{2 π}$

$I_{1} = \frac{m l^{2}}{3}, a n d I_{2} = \frac{m r^{2}}{2} = \frac{m l^{2}}{8 π^{2}}$

$\Rightarrow \frac{I_{1}}{I_{2}} = \frac{m l^{2}}{3} \times \frac{8 π^{2}}{m l^{2}} = \frac{8 π^{2}}{3}$

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