Question

Two cubes A and B has sides 10 cm and 5cm respectively are lying on a table .Find the ratio of pressure exerted by each cube on table if they have same mass 50g

Answer 1

We know that,

$\longrightarrow\sf{P=\dfrac {F}{A}}$

If both A and B have same mass they exert same force on the table, i.e., their weight.

Hence at constant force,

$\longrightarrow\sf{P\propto\dfrac {1}{A}}$

Therefore,

$\longrightarrow\sf{\dfrac {P_A}{P_B}=\dfrac {A_B}{A_A}}$

$\longrightarrow\sf{\dfrac {P_A}{P_B}=\dfrac {(L_B)^3}{(L_A)^3}}$

$\longrightarrow\sf{\dfrac {P_A}{P_B}=\left (\dfrac {L_B}{L_A}\right)^3}$

$\longrightarrow\sf{\dfrac {P_A}{P_B}=\left (\dfrac {5}{10}\right)^3}$

$\longrightarrow\sf{\underline {\underline {\dfrac {P_A}{P_B}=\dfrac {1}{8}}}}$