Gravitation Test

Result

Gravitation Test - 80

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Weekly Quiz Competition

Question 1
1 / -0

Two planet have the same average density but their radii are $${ R }_{ 1 }$$ and $${ R }_{ 2 }$$ . If acceleration due to gravity on these planets be $${ g }_{ 1 }$$ and$${ g }_{ 2 }$$ . respectively, then

A
$$\frac { { g }_{ 1 } }{ g_{ 2 } } =\frac { { R }_{ 1 } }{ { R }_{ 2 } } $$

B
$$\frac { { g }_{ 1 } }{ g_{ 2 } } =\frac { { R }_{ 2 } }{ { R }_{ 1 } } $$

C
$$\frac { { g }_{ 1 } }{ g_{ 2 } } =\frac { { { R }_{ 1 }^{ 2 } } }{ { R }_{ 2 }^{ 2 } } $$

D
$$\frac { { g }_{ 1 } }{ g_{ 2 } } =\frac { { { R }_{ 1 }^{ 3 } } }{ { R }_{ 2 }^{ 3 } } $$

Solution
Question 2
1 / -0

Two persona A and B are sitting on weighing machines arranged in two vans parked at the equatorial region. They show same reading. If A moves due west and B moves due east with a speed of 200 kmph along the equator, then

A
the weights of A and B will be same

B
the weight of A slightly increases

C
the weight of B slightly increases

D
the weight of A slightly decreases

Solution
Question 3
1 / -0

The distance between two planets of masses M and 4M is 'a' what is the gravitational potential at a point on a line joining them of which the gravitational intensity is zero?

A
$$-\frac{9GM}{r}$$

B
$$-\frac{5GM}{a}$$

C
$$-\frac{3GM}{a}$$

D
$$-\frac{7GM}{a}$$

Solution

Let the point be the position when the gravitational field in zero
$$\dfrac{Gm}{x^{2}}=\dfrac{G(4m)}{(r-x)^{2}} \Rightarrow \dfrac{1}{x} =\dfrac{2}{(r-x)}$$
$$r-2=2x \ x= r/3$$
The point $$'P'$$ is at a distance $$\dfrac{r}{3}$$ from man $$m$$ and $$\dfrac{2r}{3}$$ from man $$4m$$
$$\therefore v=\dfrac{-Gm}{r/3}-\dfrac{G(4m)}{\dfrac{2r}{3}}=\dfrac{-9Gm}{r}$$
$$v=\dfrac{-9Gm}{r}$$
Question 4
1 / -0

If $$g$$ is acceleration due to gravity on the surface of the earth$$,$$ having radius $$R,$$ the height at which the acceleration due to gravity reduces to $$g/2$$ is

A
$$R/2$$

B
$$\sqrt 2 R$$

C
$$\frac{R}{{\sqrt 2 }}$$

D
$$\left( {\sqrt 2 - 1} \right)R$$

Solution
Question 5
1 / -0

A particle of mass $$m$$ is released from a height R ( radius of earth) from the surface of earth. When it reaches the earth's surface, it enters a tunnel leading to its centre. Its speed at the centre is

A
$$\sqrt {gR} $$

B
$$\sqrt {2gR} $$

C
$$\sqrt {3gR} $$

D
$$\sqrt {5gR} $$

Solution
Question 6
1 / -0

If $$W_1,W_2$$ and $$W_3$$ represent the work done in moving a particle from A to B along three different paths 1,2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between $$W_1,W_2$$ and $$W_3$$:

A
$$ W_1 > W_2 > W_3$$

B
$$ W_1 = W_2 = W_3$$

C
$$ W_1 < W_2 < W_3$$

D
$$ W_2 > W_1 > W_3$$

Solution
Question 7
1 / -0

How much energy will be necessary for making a body of 500 Kg to escape from the earth?
$$ [ g = 10 m/s^2$$, radius of earth $$= 6.4 \times 10^6 m] $$

A
$$ 6.4 \times 10^8 J $$

B
$$ 3.2 \times 10^{10} J $$

C
$$ 6.4 \times 10^{12} J $$

D
$$ 3.2 \times 10^6 J $$

Solution
Question 8
1 / -0

The gravitational field due to a mass distribution is $$\vec {I} = \dfrac {k}{x^{3}}\hat {i}$$ where $$k$$ is a constant. Taking the gravitational potential to be zero at infinity, its value at a distance $$x= d$$ is

A
$$\dfrac {k}{2d^{2}}$$

B
$$\dfrac {k}{d^{2}}$$

C
$$\dfrac {k}{2d}$$

D
$$\dfrac {k}{d}$$

Solution
Question 9
1 / -0

An artificial earth satellite is taken from a higher orbit to a lower orbit $$ i.e.r_2 < r_1 $$. In this process,the gravitational potential energy

A
in increased

B
does not change

C
in decreased

D
is doubled

Solution
Question 10
1 / -0

The weight of a body of mass $$250\ kg$$ when it is at a height of $$4$$ times the radius of earth, from earth's surface is :

A
$$25\ N$$

B
$$50\ N$$

C
$$64\ N$$

D
$$100\ N$$

Solution