Question

Two bodies A and B made of the same material have the moment of inertia in the ratio ${I_A}:{I_B} = 16:18\,$. The ratio of the masses ${m_A}:{m_{B\,}}$is given by
A. cannot be obtained
B. $2:3$
C. $1:1$
D. $4:9$

Answer 1

Hint:Here we have to find the ratio of the masses of two bodies A and B whose ratio of moment of inertia is given. For this we need to find the relation between the moment of inertia and mass of a body. After finding the relation between the two try to put the given information from the question and see whether we are able to find the ratio of masses of the bodies.

Formula used:
The expression of moment of inertia is,
$I = m \times {k^2}$
Where, $m$ = mass of the body
$k$ = distance from the axis of rotation

Complete step by step solution:
First start the given information,
Ratio of moment of inertia of the two bodies is \[{I_A}:{I_B} = 16:18\].
Where, $I$ = moment of inertia
${I_A}$ = moment of inertia of bodyA
${I_B}$ = moment of inertia of bodyB

Now use the relation between the moment of inertia and mass of the body. For this we know the formula of moment of inertia as follows: moment of inertia is equal to the product of mass of body and square of distance of the body from the axis of the rotation.
$I = m \times {k^2}$
Since no information about the distance of the body from the axis of the rotation is not given, the ratio of the masses of the body cannot be determined. To find the mass of the body we need the value of the moment of inertia and distance from the axis. With two unknown values in an equation it is not possible to find the value of mass of the body without knowing the value of k. Hence we cannot find the ratio of masses of body as well.

Hence the correct answer is option A.

Note: To solve these questions we just need to know the basic concept and the basic formula of moment of inertia and put all the given values from the question. Here the value of k is not given. If it is given, put the value in the formula and we will get the value of mass of the body and hence the ratio of the masses of the bodies.