A man can jump to a height of $1.5 \,m$ on a planet $A$. What is the height he may be able to jump on another planet whose density and radius are, respectively, one-quarter and one-third that of planet $A$ ....... $m$
A man can jump to a height of $1.5 \,m$ on a planet $A$. What is the height he may be able to jump on another planet whose density and radius are, respectively, one-quarter and one-third that of planet $A$ ....... $m$
$1.5$
$15$
$18$
$28$
A man can jump to a height of $1.5 \,m$ on a planet $A$. What is the height he may be able to jump on another planet whose density and radius are, respectively, one-quarter and one-third that of planet $A$ ....... $m$
$H = \frac{{{u^2}}}{{2g}}\, \Rightarrow \,H \propto \frac{1}{g}$ $⇒$ $\frac{{{H_B}}}{{{H_A}}} = \frac{{{g_A}}}{{{g_B}}}$
Now ${g_B} = \frac{{{g_A}}}{{12}}\;{\rm{as}}\,\,g \propto \rho R$
$\frac{{{H_B}}}{{{H_A}}} = \frac{{{g_A}}}{{{g_B}}}=12$
$⇒$ ${H_B} = 12 \times {H_A} = 12 \times 1.5 = 18\,m$
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