Question

find the ratio of potential energies of two objects having same mass one rise at a height of h while other is rest at a height 5h​

Answer 1

We know that, potential energy,

$\displaystyle\longrightarrow\sf {U=mgh}$

But in the case of same mass,

$\displaystyle\longrightarrow\sf {U\propto h}$

Thus we form an equation,

$\displaystyle\longrightarrow\sf {\dfrac {U_1}{U_2}=\dfrac {h_1}{h_2}}$

Here it's given that,

$\displaystyle\longrightarrow\sf {h_1=h}$

$\displaystyle\longrightarrow\sf {h_2=5h}$

Therefore,

$\displaystyle\longrightarrow\sf {\dfrac {h_1}{h_2}=\dfrac {1}{5}}$

Hence,

$\displaystyle\longrightarrow\sf {\underline {\underline {\dfrac {U_1}{U_2}=\dfrac {1}{5}}}}$

Or,

$\displaystyle\longrightarrow\sf {\underline {\underline {U_1:U_2=1:5}}}$