Which of the following statements is true?

(a)  g is less at the earth's surface than at a height above it or a depth below it
(b)  g is the same at all places on the surface of the earth
(c)  g has its maximum value at the equator
(d)  g is greater at the poles than at the equator

Concept Questions :-

Acceleration due to gravity

Difficulty Level:

A spring balance is graduated on sea level. If a body is weighed with this balance at consecutively increasing heights from earth's surface, the weight indicated by the balance
(a) Will go on increasing continuously
(b) Will go on decreasing continuously
(c) Will remain same
(d) Will first increase and then decrease

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

The gravitational field due to a mass distribution is $E=K/{x}^{3}$ in the x-direction. (K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x is

(a) K/x                    (b) K/2x

(c) $K/{x}^{2}$                 (d) K/2${x}^{2}$

Concept Questions :-

Gravitational Potential
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Difficulty Level:

The change in potential energy, when a body of mass m is raised to a height nR from the earth's surface is (R = Radius of earth)

(a) $mgR\frac{n}{n-1}$                     (b) nmgR

(c) mgR $\frac{{n}^{2}}{{n}^{2}+1}$                   (d) $mgR\frac{n}{n+1}$

Concept Questions :-

Gravitational potential energy
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Difficulty Level:

The value of g on the earth's surface is 980 cm/$se{c}^{2}$ . Its value at a height of 64 km from the earth's surface is

(a)           (b)

(c)            (c) 982.45 cm/$se{c}^{2}$

(Radius of the earth R = 6400 kilometers)

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

If the earth suddenly shrinks (without changing mass) to half of its present radius, the acceleration due to gravity will be

(a)   g/2                             (b)   4g

(c)   g/4                             (d)  2g

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

The masses and radii of the earth and moon are  and  respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is

(a) $2\sqrt{\frac{G}{D}\left({M}_{1}+{M}_{2}\right)}$                  (b) $2\sqrt{\frac{2G}{D}\left({M}_{1}+{M}_{2}\right)}$

(c) $2\sqrt{\frac{GM}{D}\left({M}_{1}+{M}_{2}\right)}$               (d) $2\sqrt{\frac{GM\left({M}_{1}+{M}_{2}\right)}{D\left({R}_{1}+{R}_{2}\right)}}$

Concept Questions :-

Gravitational potential energy
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Difficulty Level:

If mass of earth is M, radius is R and gravitational constant is G, then work done to take 1 kg mass from earth surface to infinity will be

(a)    $\sqrt{\frac{GM}{2R}}$                            (b)

(c)     $\sqrt{\frac{2GM}{R}}$                         (d)   $\frac{GM}{2R}$

Concept Questions :-

Gravitational potential energy
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Difficulty Level:

If ${v}_{e}$ and ${v}_{o}$ represent the escape velocity and orbital velocity of a satellite corresponding to a circular orbit of radius R, then

(a) ${v}_{e}={v}_{o}$                      (b) $\sqrt{2}{v}_{o}={v}_{e}$

(c) ${v}_{e}={v}_{o}/\sqrt{2}$               (d) ${v}_{e}$ and ${v}_{o}$ are not related

Concept Questions :-

Escape velocity
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Difficulty Level:

If r represents the radius of the orbit of a satellite of mass m moving around a planet of mass M, the velocity of the satellite is given by:

(a) ${v}^{2}=g\frac{M}{r}$                      (b) ${v}^{2}=\frac{GMm}{r}$

(c) $v=\frac{GM}{r}$                        (d) ${v}^{2}=\frac{GM}{r}$

Concept Questions :-

Satellite