If a planet consists of a satellite whose mass and radius were both half that of earth, acceleration

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7.Gravitation

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If a planet consists of a satellite whose mass and radius were both half that of the earth, the acceleration due to gravity at its surface would be ......... $m/{\sec ^2}$ ($ g$ on earth $= 9.8\, m/sec^2$ )

$4.9$

$8.9$

$19.6$

$29.4$

Solution

According to problem ${M_p} = \frac{{{M_e}}}{2}$ and ${R_p} = \frac{{{R_e}}}{2}$

$\therefore$ $\frac{{{g_p}}}{{{g_e}}} = \left( {\frac{{{M_p}}}{{{M_e}}}} \right)\;{\left( {\frac{{{R_e}}}{{{R_p}}}} \right)^2} = \left( {\frac{1}{2}} \right)\; \times {(2)^2} = 2$

==> ${g_p} = 2{g_e} = 2 \times 9.8 = 19.6\;m/{s^2}$

Standard 11

Physics

Spot the wrong statement :The acceleration due to gravity $‘g’$ decreases if

easy

A body weighs $72 N$ on surface of the earth. When it is taken to a height of $h=2 R$, where $R$ is radius of earth, it would weigh …….. $N$

easy

Two satellites $\mathrm{P}$ and $\mathrm{Q}$ are moving in different circular orbits around the Earth (radius $R$ ). The heights of $\mathrm{P}$ and $\mathrm{Q}$ from the Earth surface are $h_{\mathrm{p}}$ and $h_{\mathrm{Q}}$, respectively, where $h_{\mathrm{p}}=\mathrm{R} / 3$. The accelerations of $\mathrm{P}$ and $\mathrm{Q}$ due to Earth's gravity are $g_{\mathrm{p}}$ and $g_{\mathrm{Q}}$, respectively. If $g_{\mathrm{p}} / g_{\mathrm{Q}}=36 / 25$, what is the value of $h_Q$ ?

medium

(IIT-2023)

Explain the variations of acceleration due to gravity inside and outside the earth and draw the graph.

hard

The value of the acceleration due to gravity is $g _{1}$ at a height $h =\frac{ R }{2}( R =$ radius of the earth) from the surface of the earth. It is again equal to $g _{1}$ at a depth $d$ below the surface of the earth. The ratio $\left(\frac{ d }{ R }\right)$ equals