Question

From a given sample of uniform wire, two circular loops P and Q are made, P of radius r and Q of radius nr. If the moment of inertia of Q about its axis is four times that of P about its axis (assuming wire diameter to be much smaller than either radius), the value of n is

• A. $(4{)}^{\frac{2}{3}}$
• B. $(4{)}^{\frac{1}{3}}$
• C. $(4{)}^{\frac{1}{2}}$
• D. $(4{)}^{\frac{1}{4}}$

Answer 1

The correct option is B $(4{)}^{\frac{1}{3}}$

$I_Q=m_Q(nr{)}^2=\mu (2\pi nr\left)\right(nr{)}^2[\mu :lineardensity]=2\pi \mu n^3{r}^{3}ForwireP,I=m{r}^2=\mu \left(2\pi r\right)r=2\pi \mu r^3{I}_Q=4Ip2\pi \mu n^3{r}^3=8\pi \mu r^3\Rightarrow n=(4{)}^{\frac{1}{3}}$