Question

a wheel of mass 10kg has a moment of inertia of 160kgm^2 about its own axis the radius of gyration will be?
a) 10m
b) 8m
c) 6m
d) 4m


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Answer 1

Given :-

Mass of the wheel = 10 kg

Momentum of inertia = 160 kg/m²

To Find :-

The radius of gyration.

Analysis :-

Here we are given with the mass and the momentum of inertia.

In order to find the radius of gyration substitute the given values from the question in the formula of momentum of inertia.

Solution :-

We know that,

• i = Momentum of inertia
• m = Mass
• k = Radius

Using the formula,

$\underline{\boxed{\sf Momentum \ of \ inertia=MK^2}}$

Given that,

Mass (m) = 10 kg

Momentum of inertia (i) = 160 kg/m²

Substituting their values,

⇒ 160 = 10 × k²

⇒ k² = 160/10

⇒ k² = 16

⇒ k = √16

⇒ k = 4 m

Therefore, the radius of gyration is (d) 4 m.

Answer 2

Answer:

Answer

$\sf \purple{ \dashrightarrow} \bf \red{4 \: m}$

Explanation:

Given :-

• Mass of wheel = 10 kg
• Moment of Interia = 160 kg/m²

To Find :-

Radius of gyration

Solution :-

$\boxed{ \bf \: Moment \: of \: Interia = MK {}^{2} }$

Here,

M is the Mass

K is the Radius of gyration

I is the moment of Interia

$\sf \: 160 = 10 \times {k}^{2}$

$\sf {k}^{2} = \dfrac{160}{10}$

$\tt \: {k }^{2} = 16$

$\sf \: k \: = \sqrt{16}$

$\frak \green{k \: = 4m}$

Therefore :-

Option D is correct