Frequency $f$ of a simple pendulum depends on its length $\ell$ and acceleration $g$ due to gravity according to the following equation $f=\frac{1}{2 \pi} \sqrt{\frac{ g }{\ell}}$. Graph between which of the following quantities is a straight line?
$f$ on the ordinate and $\ell$ on the abscissa
$f$ on the ordinate and $\sqrt{ \ell }$ on the abscissa
$f ^2$ on the ordinate and $\ell$ on the abscissa
$f ^2$ on the ordinate and $1 / \ell$ on the abscissa
A particle moves along the straight line $y=3 x+5$. Which coordinate changes at a faster rate?
If $log_{10} (xy) = 2$, then the value of $xy$ is
The area $'A'$ of a blot of ink is growing such that after $t$ second its area is given by $A = (3t^2 + 7)\,cm^2$. Calculate the rate of increase of area at $t = 2\, sec$. .......... $cm^2/s$
A particular straight line passes through origin and a point whose abscissa is double of ordinate of the point. The equation of such straight line is :
The coordinates of a particle moving in $XY$-plane vary with time as $x=4 t ^2 ; y=2 t$. The locus of the particle is a :-