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: Approach
Use the standard results for tangential axes.

Step 2: Known values
Solid sphere about a tangent: $\dfrac75MR^2$. Disc about a tangent in its plane: $\dfrac54MR^2$.

Step 3: Insert masses
Sphere: $\dfrac75\times5=7$ (in units of $R^2$). Disc: $\dfrac54\times4=5$.

Step 4: Ratio
$7:5$, so $x=7$, $y=5$. 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). \[ \boxed{7,\ 5} \]