What is the intensity of gravitational field of the centre of a spherical shell ?

(a)     $Gm/{r}^{2}$           (b)    g

(c)      Zero              (d)    None of these

Concept Questions :-

Gravitational field

Difficulty Level:

The depth d at which the value of acceleration due to gravity becomes $\frac{1}{n}$  times the value at the surface, is [R = radius of the earth]

(a) $\frac{R}{n}$                              (b)  $R\left[\frac{n-1}{n}\right]$

(c) $\frac{R}{{n}^{2}}$                             (d) $R\left[\frac{n}{n+1}\right]$

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Difficulty Level:

The diameters of two planets are in the ratio 4 : 1 and their mean densities in the ratio 1 : 2. The acceleration due to gravity on the planets will be in ratio

(a)  1 : 2                             (b)  2 : 3

(c)   2 : 1                            (d)  4 : 1

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

At what altitude in metre will the acceleration due to gravity be 25% of that at the earth's surface (Radius of earth = R metre)

(a)$\frac{1}{4}R$                           (b)  R

(c)   $\frac{3}{8}R$                          (d) $\frac{R}{2}$

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

The gravitational potential energy of a body of mass ‘m’ at the earth’s surface $-mg{R}_{\mathcal{e}}$. Its gravitational potential energy at a height ${R}_{\mathcal{e}}$ from the earth’s surface will be (Here ${R}_{\mathcal{e}}$  is the radius of the earth)

(a)       $-2mg{R}_{\mathcal{e}}$              (b)        $2mg{R}_{\mathcal{e}}$

(c)       $\frac{1}{2}mg{R}_{\mathcal{e}}$               (d)        $-\frac{1}{2}mg{R}_{\mathcal{e}}$

Concept Questions :-

Gravitational potential energy
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Difficulty Level:

If the angular speed of the earth is doubled, the value of acceleration due to gravity (g) at the north pole

(a) Doubles                   (b)  Becomes half

(c)  Remains same        (d)   Becomes zero

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

Escape velocity of a body of 1 kg mass on a planet is 100 m/sec. Gravitational Potential energy of the body at the planet is -

(a)   – 5000 J                      (b)  – 1000 J

(c)   – 2400 J                       (d)  5000 J

Concept Questions :-

Gravitational potential energy
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Difficulty Level:

At the surface of a certain planet, acceleration due to gravity is one-quarter of that on earth. If a brass ball is transported to this planet, then which one of the following statements is not correct ?

(a)     The mass of the brass ball on this planet is a quarter of its mass as measured on earth

(b)  The weight of the brass ball on this planet is a quarter of the weight as measured on earth

(c)   The brass ball has the same mass on the other planet as on earth

(d)  The brass ball has the same volume on the other planet as on earth

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

A body of mass m is placed on the earth’s surface. It is taken from the earth’s surface to a height 3R . The change in gravitational potential energy of the body is -

(a)   $\frac{2}{3}mgR$                      (b) $\frac{3}{4}mgR$

(c)    $\frac{mgR}{2}$                       (d) $\frac{mgR}{4}$

Concept Questions :-

Gravitational potential energy
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Difficulty Level:

Weight of 1 kg becomes 1/6 kg on moon. If radius of moon is $1.768×{10}^{6}m$, then the mass of moon will be -

(a) $1.99×{10}^{30}kg$                        (b) $7.56×{10}^{22}kg$

(c) $5.98×{10}^{24}kg$                       (d) $7.65×{10}^{22}kg$

Concept Questions :-

Acceleration due to gravity