Question

2. The moment of ineritia of an obfect about
am aris in 200kg-m2. What is the reduis
gyreation of the object about the anis?
Weight of the object in 19.6N.​

Answer 1

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).

$:\implies I \sf = MK^2$

$:\implies \sf200 = 2 \times K^2$

$:\implies \sf K^2 = \dfrac{200}{2}$

$:\implies \sf K^2 = 100$

$:\implies \sf K = \sqrt{100}$

$:\implies \underline{ \boxed{\sf K = 10 \: m}}$

Answer 2

${ \underline{ \underline{ \rm{ \orange{ \huge{QUESTION}}}}}}$

The moment of inertia of an object about an axis is 200 kg m^2 . What is the radius of gyration of the object about the axis ?

Weight of the object is 19.6 N.

${ \underline{ \underline{ \rm{ \orange{ \huge{SOLUTION}}}}}}$

${ \leadsto{ \underline{ \underline{ \rm{ \pink{given}}}}}} \\ \\ { \dashrightarrow{ \sf{ \blue{moment \: of \: inertia(l) = 200 \: kg \: {m}^{2} }}}} \\ \\ { \dashrightarrow{ \sf{ \blue{ \: weight \: of \: object \: (w) = 19.6 \:N}}}}$

${ \leadsto{ \underline{ \underline{ \rm{ \pink{to \: find}}}}}} \\ \\ { \sf{ \: radius \: of \: gyration \: (k) \: .}}$

${ \boxed{ \boxed{ \sf{ \green{weight(w)= mass(m) \times acceleration(g)}}}}} \\ \\ { \rightarrow{ \sf{ mass(m) = \frac{w}{g} }}} \\ \\ { \rightarrow{ \sf{ mass(m) = \frac{19.6 \:N }{9.8 \: m \: {sec}^{ - 2} } }}} \\ \\ { \rightarrow { \boxed{ \boxed{ \red{ \sf{mass(m) = 2 \: kg}}}}}}$

${ \sf { \underline{ \blue{using\: the\: formula}}}} \\ \\ { \underline{ \boxed{ \green{ \sf{(l) = m \: \times \: {k}^{2} }}}}} \\ \\ { \rightarrow{ \sf{ {k}^{2} = \frac{l}{m} }}}$

${ \rightarrow{ \sf{ {k}^{2} = \frac{200 \: kg \: {m}^{2} }{2 \: kg}}}} \\ \\ { \rightarrow{ \sf{ {k}^{2} = 100 \: {m}^{2} }}} \\ \\ { \rightarrow{ \sf{k = \sqrt{100 \: {m}^{2} } }}}$

${ : { \implies{ \underline{ \boxed{ \sf{ \red{radius \: of \: gyration(k) = 10 \: m}}}}}}}$