Gravitation Test

Result

Gravitation Test - 83

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Question 1
1 / -0

A particle is released from a very large separation from a sphere of mass $$m$$ and radius $$R$$. In which a tunnel is present. Find the ratio of speed acquired by the particle as it reaches the center of the sphere to that of as it reaches its surface.

A
$$\sqrt{2}$$

B
$$\sqrt{\dfrac{1}{2}}$$

C
$$\sqrt{\dfrac{3}{2}}$$

D
$$\sqrt{\dfrac{2}{3}}$$

Solution
Question 2
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In the usual notation, the acceleration due to gravity at a height $$h$$ from the surface of the earth is .........

A
$$g= \frac{GM}{R+h}$$

B
$$g= \frac{GM}{\sqrt{R+h}}$$

C
$$g= \frac{GM}{(R+h)^2}$$

D
$$g= GM(R+h)^2$$

Solution
Question 3
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The value of the acceleration due to gravity at a height from Earth's surface decreases by $$1\%$$. What will be the value of height from the surface?(Take the radius of earth =$$6400\ km$$)

A
$$32\ km$$

B
$$24\ km$$

C
$$14\ km$$

D
$$40\ km$$

Solution
Question 4
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The change in the value of $$^ { \prime } g ^ { \prime }$$ at a height $$^ { \prime }$$ h'above the surface of the earth is same as at a depth 'd'. If d and h are much smaller than the radius of earth, then which one of the following is correct?

A
$$d=h$$

B
$$d=2h$$

C
$$d = \frac { 3 h } { 2 }$$

D
$$d = h / 2$$

Solution
Question 5
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A particle would take a time $$t$$ to move down a straight tube from the surface of earth (supposed to be a homogeneous sphere) to its centre. If gravity were to remain constant, then the time would be $$t$$. The ratio of $$t/t$$ will be

A
$$\dfrac{ \pi }{ 2\sqrt { 2 } }$$

B
$$\dfrac{ \pi }{ \sqrt { 2 } }$$

C
$${ \sqrt { 2 }\pi }$$

D
$$\dfrac{ \pi }{ \sqrt { 2 } }$$

Solution
Question 6
1 / -0

A satellite is revolving around Earth in a circular orbit whose radius is R.work done by gravitational force in one revolution is

A
zero

B
2$$\mathrm { mgR } ^ { 2 }$$

C
$$\mathrm { mgR } ^ { 2 }$$

D
$$\mathrm { mgR }$$

Solution
Question 7
1 / -0

Suppose the acceleration due to gravity at the earth's surface is $$10 \mathrm { m } / \mathrm { s } ^ { 2 }$$ and at the surface of mars it is $$4.0 \mathrm { m } / \mathrm { s } ^ { 2 } .$$ A $$60 \mathrm { kg }$$ passenger goes from the earth to the mars in a spaceship moving with a constant velocity. Neglect all other object in the sky. Which part of the figure best represent the weight (net gravitational force) of the passenger as a function of time?

A
$$A$$

B
$$B$$

C
$$C$$

D
$$D$$

Solution

Note that there must be some point where the gravitational field of the earth is balanced by the gravitational field of Mars.
Question 8
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The acceleration due to gravity at a height $$1 km$$ above the earth is the same as at a depth $$d$$ below the surface of earth. Then

A
$$d = 1 \mathrm { km }$$

B
$$d = \dfrac { 3 } { 2 } k m$$

C
$$d = 2 \mathrm { km }$$

D
$$d = \dfrac { 1 } { 2 } k m$$

Solution
Question 9
1 / -0

A man is standing on an international space station, which is orbiting earth at an altitude 520$$\mathrm { km }$$ with a constant speed 7.6 $$\mathrm { km } / \mathrm { s }$$ . If the men's weight is 50$$\mathrm { kg }$$ , his acceleration is

A
76$$\mathrm { km } / \mathrm { s } ^ { 2 }$$

B
7.6$$m / s ^ { 2 }$$

C
8.4$$m / s ^ { 2 }$$

D
10$$m / s ^ { 2 }$$

Solution
Question 10
1 / -0

Wt. of body at height equal to radius of earth

A
weight on earth

B
$$\dfrac{4}{3}$$ of wt. on earth

C
Double that of wt. of earth

D
$$\dfrac{1}{4}$$ on wt. on earth

Solution