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(1/r2−1/r1) is more/less accurate than the formula mg(r2−r1) for the difference of potential energy between two points r2 and r1 distance away from the center of the earth.

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(1/r2​−1/r1​) is more/less accurate than the formula mg(r2​−r1​) for the difference of potential energy between two points r2​ and r1​ distance away from the center of the earth.

Filo · Accepted Answer

(a) Acceleration decreases according to formula

g^{'} = g (1 - \frac{2 h}{R})

,
where h is height and R is radius of earth.

(b) Acceleration decreases according to formula

g^{'} = g (1 - \frac{d}{R})

,

where d is depth and R is radius of earth.

(c) Acceleration due to gravity is given by the formula:

g = \frac{G M _{e}}{R _{e}^{2}}

Hence, it is independent of mass of body, but is dependent on mass of earth.

(d) Gravitational potential energy is given by the formula:

U = - \frac{G m _{1} m _{2}}{r}

g = \frac{G M _{e}}{R _{e}^{2}}

assuming distance between object and earth is nearly equal to the radius of the earth.

Substituting the second equation in first, we get

U \approx m g h

Hence, the first formula is more accurate.

Question Text	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 $- G M m (1/ r_{2} - 1/ r_{1})$ is more/less accurate than the formula $m g (r_{2} - r_{1})$ for the difference of potential energy between two points $r_{2}$ and $r_{1}$ distance away from the center of the earth.
Answer Type	Text solution:1
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