Solve the following :

The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius. Find the distance of the line from the centre.


$I_{a x i s}=I_{C O M}+m d^{2}$

$m k^{2}=\frac{m r^{2}}{2}+m d^{2}$

$\Rightarrow m r^{2}=\frac{m r^{2}}{2}+m d^{2}$

$\Rightarrow d=\sqrt{2}$

Solve the following

(i) Is 68 a term of the A.P. 7, 10, 13, …?

(ii) Is 302 a term of the A.P. 3, 8, 13, …?


(i) 7, 10, 13…

Here, we have:

a = 7


Let $a_{n}=68$

$\Rightarrow a+(n-1) d=68$

$\Rightarrow 7+(n-1)(3)=68$



$\Rightarrow n=\frac{61}{3}+1=\frac{64}{3}$

Since n is not a natural number.So, 68 is not a term of the given A.P.

(ii) 3, 8, 13…

Here, we have:

a  = 3


Let $a_{n}=302$

$\Rightarrow a+(n-1) d=302$

$\Rightarrow 3+(n-1) 5=302$

$\Rightarrow(n-1) 5=299$


$\Rightarrow n=\frac{299}{5}+1=\frac{304}{5}$

Since n is not a natural number.So, 302 is not a term of the given A.P.








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