2. The moment of ineritia of an obfect aboutam aris in 200kg-m2. What

1.	2. The moment of ineritia of an obfect aboutam aris in 200kg-m2. What is the reduisgyreation of the object about the anis?Weight of the object in 19.6N.
Answer» TOPIC :- Rotational Dynamics $\maltese\:\underline{\sf AnsWer :}\:\maltese$ Moment of inertia (I) = 200 kg-m² Weight of the object (F) = 19.6 N Radius of gyration (K) = ? To calculate the radius of gyration about an axis we will use the GIVEN below formula : $:\implies I \sf = MK^2 \\$ But here first we need to find the mass of the object. So, LET's first find the mass of the object $\longrightarrow\:\:\sf F = mg \\$ $\longrightarrow\:\:\sf m = \dfrac{F}{g} \\$ $\longrightarrow\:\:\sf m = \dfrac{19.6}{9.8} \\$ $\longrightarrow\:\: \underline{ \boxed{\sf m = 2 \: kg}} \\$ Hence, the mass (M) of the object is 2 kg. Now, let's find the radius of gyration (K). $:\implies I \sf = MK^2 \\$ $:\implies \sf200 = 2 \times K^2 \\$ $:\implies \sf K^2 = \dfrac{200}{2} \\$ $:\implies \sf K^2 = 100\\$ $:\implies \sf K = \sqrt{100} \\$ $:\implies \underline{ \boxed{\sf K = 10 \: m}}$