The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is . The length of the 400 g rod is nearly [2024]

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Solution

Q.
The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is $2400 g$ ${cm}^{2}$ . The length of the 400 g rod is nearly [2024]

1 8.5 cm

2 17.5 cm

3 20.7 cm

4 72.0 cm

Ans.
(1)

Moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod

$I_{cm} = \frac{M l^{2}}{12}$ ...(i)

where, M = Mass of the rod, $l$ = Length of the rod

Given, $M = 400 g,$ $l = ?, I_{cm} = 2400$ $g$ ${cm}^{2}$

From eq (i), $l = \sqrt{\frac{I_{cm} \times 12}{M}} = \sqrt{\frac{2400 \times 12}{400}} = 8.484 \approx 8.5 cm$

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