Question 599: Centre of Mass and Rotational Motion

Question

Two circular loop $A$ and $B$ of radii $R$ and $N R$ respectively are made from a uniform wire. Moment of inertia of $B$ about its axis is 3 times that of $A$ about its axis. The value of $N$ is

Accepted Answer

Given, $r_A=R$ and $r_B=N R$
Mass of wire $A, m_A=2 \pi r_A ho=2 \pi R ho$
Mass of wire $B, m_B=2 \pi r_B ho=2 \pi N R ho=N m_A$
The moment of inertia of a circular loop is
$$I=m r^2$$
$$\begin{aligned}
& 	ext { Here, } \quad I_B=3 I_A \
& m_B r_B^2=3 	imes m_A r_A^2 \
& \Rightarrow \quad N m_A(N R)^2=3 m_A(R)^2 \
& \Rightarrow \quad N^3=3 	ext { or } N=(3)^{1 / 3}
\end{aligned}$$

Answer

$[2]^{\frac{1}{3}}$

Answer

$[5]^{\frac{1}{3}}$

Answer

$[3]^{\frac{1}{3}}$

Answer

$[4]^{\frac{1}{3}}$

Centre of Mass and Rotational Motion

Two circular loop A and B of radii R and N R respectively are made from a uniform wire. Moment of inertia of B about its axis is 3 times that of A about its axis. The value of N is

Choose the correct answer: