From a given sample of uniform wire, two circular loops P and Q are made, P of radius r and Q of radius n r. If the M.I. of Q about its axis is 4 times that of P about its axis (assuming wire diameter much smaller than either radius of the loops), the value of n is:

Question

From a given sample of uniform wire, two circular loops P and Q are made, P of radius r and Q of radius n r. If the M.I. of Q about its axis is 4 times that of P about its axis (assuming wire diameter much smaller than either radius of the loops), the value of n is: (A) (4)2 / 3 (B) (4)1 / 3 (C) (4)1 / 2 (D) (4)1 / 4

Tardigrade Admin · Accepted Answer

IP=m r2, IQ=(n m)(n r)2=n3 m r2 Now IQ=4 IP ⇒ n3 m r2=4 m r2 ⇒ n=(4)1 / 3

Q. From a given sample of uniform wire, two circular loops $P$ and $Q$ are made, $P$ of radius $r$ and $Q$ of radius $n r$ . If the M.I. of $Q$ about its axis is 4 times that of $P$ about its axis (assuming wire diameter much smaller than either radius of the loops), the value of $n$ is:

$(4)^{2/3}$

$(4)^{1/3}$

$(4)^{1/2}$

$(4)^{1/4}$

$I_{P} = m r^{2}, I_{Q} = (nm) (n r)^{2} = n^{3} m r^{2}$
Now $I_{Q} = 4 I_{P} \Rightarrow n^{3} m r^{2} = 4 m r^{2}$
$\Rightarrow n = (4)^{1/3}$

Q. 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 M.I. of Q about its axis is 4 times that of P about its axis (assuming wire diameter much smaller than either radius of the loops), the value of n is:

(4)2/3

(4)1/3

(4)1/2

(4)1/4