Gravitation Test

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Gravitation Test - 68

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Weekly Quiz Competition

Question 1
1 / -0

The gravitational potential at the centre of a square of side a when four point masses m each are kept at its vertices will be

A
$$4 \sqrt{2} \dfrac{Gm}{a}$$

B
$$-4 \sqrt{2} \dfrac{Gm}{a}$$

C
$$2 \sqrt{2} \dfrac{Gm}{a}$$

D
$$-2 \sqrt{2} \dfrac{Gm}{a}$$

Solution

$$\begin{array}{l} AO=\dfrac { { \sqrt { 2 } a } }{ 2 } =\dfrac { a }{ { \sqrt { 2 } } } \\ V=\dfrac { { -Gm } }{ r } \\ { V_{ net } }=\dfrac { { -4Gm } }{ r } =\dfrac { { -4Gm } }{ { \dfrac { a }{ { \sqrt { 2 } } } } } =\dfrac { { -4\sqrt { 2 } Gm } }{ a } \end{array}$$.
$$\therefore$$ Option $$B$$ is correct.
Question 2
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Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will.

A
Will become statioanry

B
Keep floating at the same distance between them

C
Move away from each other

D
Move towards from each other

Solution
Question 3
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The gravitational force between two point masses $${ m }_{ 1 }$$ and $${ m }_{ 2}$$ at separation r is given by
$$F=k\dfrac { { m }_{ 1 }{ m }_{ 2 } }{ { r }^{ 2 } } .$$
The constant k depends on :

A
Depends on system of units only

B
Depends on medium between masses only

C
Depends on both (a) and (b)

D
is independent of both (a) and (b)

Solution
Question 4
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How much percentage change in acceleration due gravity on an object occurs if object is initially at '2R' distance above the surface of the earth and falls through 'R' distance? (Here, R is the radius of earth)

A
decrease by 300%

B
increase by 300%

C
decrease by 125%

D
increase by 125%

Solution
Question 5
1 / -0

The radius of the Earth shrinks by $$1$$%, its mass remaining the same. The percentage change in the value of $$g$$ on surface of earth is

A
$$-2$$%

B
$$+2$$%

C
$$-3$$%

D
$$+4$$%

Solution
Question 6
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IF the acceleration due to gravity, $$g$$, is 10m/$${ s }^{ 2 }$$ at the surface of the earth (radius $$6400 km$$ ), then at a height of $$1600 m$$ the value of $$g$$ will be (in m/$${ s }^{ 2 }$$)

A
$$9.995$$

B
$$5$$

C
$$7.5$$

D
$$2.5$$

Solution
Question 7
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If the earth were to cases rotating about its own axis. The increase in the value of g in CGS system at a place of latitude of $${ 45 }^{ o }$$ will be

A
$$2.68$$

B
$$1.69$$

C
$$3.36$$

D
$$0.34$$

Solution
Question 8
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A bird weighing $$1kg$$ is sitting on the base of cage weighing $$1.5kg$$. The bird strarts flying inside the cage the weight of the bird cage assembly will now be:

A
infinite

B
$$2.5kg$$

C
$$3.5$$

D
$$1kg$$

Solution
Question 9
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If the radius of the earth is 6400 km and g = 10 $${ m/s }^{ 2 }$$, the escape velocity from the earth is

A
$$8$$ $$km/s$$

B
$$8\sqrt { 2 } $$ $$km/s$$

C
$$8/\sqrt { 2 } $$ $$km/s$$

D
None of these

Solution
Question 10
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If a ball is projected with a velocity equal to 1/4th of the escape velocity from the surface of the earth. the height it will attain is ___________ [ R : Radius of Earth]

A
$$\dfrac{R}{4}$$

B
$$\dfrac{R}{32}$$

C
$$4R$$

D
$$\dfrac{R}{16}$$

Solution

from newton's eqn. of motion
$$h = \dfrac{v^2}{2g}$$
$$v = v_{esc} = \sqrt{2gR}$$
as per question
$$h = \dfrac{\left(\dfrac{1}{4}\sqrt{2gR}\right)^2}{2g} = \dfrac{2gR}{32g}$$
$$h = \dfrac{R}{16}$$