(A) The acceleration due to gravity at height $h$ is given by $g_h = g(1 - \frac{2h}{R})$.The fractional decrease in weight at height $h$ is $\frac{\D

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(A) The acceleration due to gravity at height $h$ is given by $g_h = g(1 - \frac{2h}{R})$.The fractional decrease in weight at height $h$ is $\frac{\Delta g}{g} = \frac{2h}{R} = 1\% = 0.01$.Therefore,$\frac{h}{R} = 0.005$.The acceleration due to gravity at depth $h$ is given by $g_d = g(1 - \frac{h}{R})$.The fractional decrease in weight at depth $h$ is $\frac{\Delta g}{g} = \frac{h}{R} = 0.005 = 0.5\%$.Thus,the weight of the body decreases by $0.5\%$.

Class 11 Physics Gravitation Acceleration Due to Gravity and its Variation

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Weight of a body of mass $m$ decreases by $1\%$ when it is raised to height $h$ above the Earth's surface. If the body is taken to a depth $h$ in a mine,then its weight will

A
decrease by $0.5\%$
B
decrease by $2\%$
C
increase by $0.5\%$
D
increase by $1\%$

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Gravitation

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Acceleration Due to Gravity and its Variation

If the change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below it,then (both $x$ and $h$ being much smaller than the radius of the earth)

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The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth, assumed to be a sphere of radius $R$ of uniform density, is as shown in which of the following figures?

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If a man at the equator would weigh $(3/5)^{th}$ of his weight,the angular speed of the earth is

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Obtain an expression for the variation in effective gravitational acceleration $g'$ with latitude due to the Earth's rotation.

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The mass of a planet is $\frac{1}{10}$ that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is: (in $m \ s^{-2}$)

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Weight of a body of mass $m$ decreases by $1\%$ when it is raised to height $h$ above the Earth's surface. If the body is taken to a depth $h$ in a mine,then its weight will

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