Question

A solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. The ratio of moment of inertia of the sphere about its tangent to the moment of inertia of the disc about a tangent in its plane will be \(x:y\). The value of \(x\) and \(y\) respectively is

• A. \(5,8\)
• B. \(6,7\)
• C. \(7,5\)
• D. \(4,3\)

Hint:

Use the parallel axis theorem for each body about its tangent.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Moment of inertia about a tangent is found with the parallel axis theorem: \(I=I_{cm}+Mr^2\), because the tangent is at distance \(r\) from the centre.

Step 2: Solid sphere (mass 5 kg)
\[ I_{cm}=\frac25Mr^2,\quad I_{tan}=\frac25Mr^2+Mr^2=\frac75Mr^2=\frac75(5)r^2=7r^2 \]

Step 3: Disc (mass 4 kg), tangent in its plane
The axis through the centre along a diameter has \(I=\frac14Mr^2\). So
\[ I_{tan}=\frac14Mr^2+Mr^2=\frac54Mr^2=\frac54(4)r^2=5r^2 \]

Step 4: Ratio
\[ x:y=7r^2:5r^2=7:5 \]
So \(x=7\) and \(y=5\), option (C).

Final Answer:
The sphere gives 7 r squared and the disc gives 5 r squared, so x = 7 and y = 5, option (C). \[ \boxed{7,\ 5} \]