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PART - 1 CH - 7 Gravitation — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsPART - 1 CH - 7 Gravitation4 Marks
Question
Choose the correct alternative :
(a) Acceleration due to gravity increases/ decreases with increasing altitude.
(b) Acceleration due to gravity increases/ decreases with increasing depth (assume the earth to be a sphere of uniform density).
(c) Acceleration due to gravity is independent of mass of the earth/mass of the body.
(d) The formula - GMm $\left(1 / r_2-1 / r_1\right)$ is more/ less accurate than the formula $m g\left(r_2-r_1\right)$ for the difference of potential energy between two points $r_2$ and $r_1$ distance away from the centre of the earth.
✓

Answer

(a) Gravitational acceleration decreases with increasing altitude.
$\because$ Acceleration due to gravity at height $h$
$
g_h=g\left(1-\frac{2 h}{R}\right)
$
Hence as h increases, the value of $g_h$ decreases.
(b) The acceleratrion due to gravity decreases with increasing depth (assuming the earth is a sphere of uniform density).
$\because \quad g_d=\left(1-\frac{d}{ R }\right)$
Hence as $d$ increases the value of gravitational acceleration $g_d$ decreases.
(c) $\because$ Gravitation acceleration $g=\frac{ GM }{ R ^2}$, where M is mass of Earth.
$\therefore$ Acceleration due to gravity does not depend on mass (m) of the object.
(d) The formula of potential energy difference between two points at distance $r_2$ and $r_1$ from the center of Earth is
-GM $m\left(\frac{1}{r_2}-\frac{1}{r_1}\right)$ more accurate than the formula $m g\left(r_2-r_1\right)$.
The value of $g$ keep changing in different situations.

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