Gravitation Test

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Gravitation Test - 52

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Weekly Quiz Competition

Question 1
1 / -0

In a planet's motion around a sun, if the eccentricity of the orbit increases, then

A
planet moves in an hyperbolic path

B
planet moves in a parabolic path

C
planet moves in a straight line path

D
planet moves in a circular path

Solution

The shape of a planet's orbit depends on the eccentricity of the orbit

if the eccentricity is zero, shape is a circle
if the eccentricity is one, shape is a parabola
if the eccentricity is greater than 1, shape is a hyperbola

Thus, option (a) is the correct option
Question 2
1 / -0

The gravitational potential energy is the

A
work done in bringing an object from infinity to radius r

B
work done in moving an object around the earth

C
work done by an object in attaining an object's acceleration equal to $$9.8 m/s^2$$

D
work done in moving an object between two points horizontally

Solution

The gravitational potential energy is the work done in bringing an object from infinity to radius r

The correct option is (a)
Question 3
1 / -0

The weight (W) of an object at a depth of R/4 from the surface of the earth will be (R is the radius of the earth)

A
Zero

B
W/4

C
W/2

D
W

Solution

The apparent acceleration due to gravity at a depth d is given by $$g'=g(1-d/R)$$.Substituting d=R/4, we get g' = g/4

Thus the apparent weight becomes W/4

The correct option is (b)
Question 4
1 / -0

Gravitational potential energy is

A
the product of force and velocity

B
the product of force and momentum

C
the product of weight and height lifted by an object

D
the product of force and displacement, if the particle is moving in a cirlce

Solution

Explanation:

The product of weight and the height to which it has been elevated above the surface of the earth is gravitational potential energy.
The expression of gravitational potential energy is defined as,
$$U=mgh$$
Question 5
1 / -0

A particle of mass M is placed at origin and a small mass m is placed at A, at a distance of r from M. A force F is applied to m to make it move from A to a nearby point B. When the force becomes zero, it is observed that the mass m moves from B back to A. This is due to the reason

A
Potential of B is larger than potential of A

B
Objects starts moving in gravitational field until constant potential difference exist

C
The line B to A is equipotential surface

D
The mass moves from B to A, since A is nearer to origin

Solution

The potential of a particle is given by $$V = -GM/R$$, M is the mass of the object that exerts gravitational potential

A flow is constituted only, if it is present along a potential gradient and this flow will take place in the direction from a region of higher potential to a lower one,

As seen from the formula, $$r_B >r_A \implies V_B>V_A$$ (because of the negative sign in the potential). Thus, particle moves from B to A

The correct option is (a)
Question 6
1 / -0

The areal velocity of an object of mass m=2 kg revolving around another object is given by $$2m^2/s$$, what is the angular momentum of the particle

A
$$6 kg-m^2/s$$

B
$$8 kg-m^2/s$$

C
$$4 kg-m^2/s$$

D
$$2 kg-m^2/s$$

Solution

The areal velocity of a planet is related to its Angular momentum by the equation areal velocity = 2m x areal velocity

Substituting the values, we get, areal velocity= $$8 kg-m^2/s$$

The correct option is (b)
Question 7
1 / -0

A planet revolves around the sun in an orbit with an eccentricty = 0.99, the orbit is:

A
almost circular

B
almost elliptical

C
almost straight

D
parabolic

Solution

Eccentricity of a circle $$=0$$
Eccentricity of an ellipse $$=$$ between $$0$$ to $$1$$
Eccentricity of a hyperbola $$>1$$
Eccentricity of a straight line $$=$$ infinite
Eccentricity of a parabola $$=1$$
So, the orbit will be parabola as $$[0.99\sim 1]$$
Question 8
1 / -0

Kepler's first law provides information about

A
areal velocity of a planet

B
Shape of the orbit of the planet

C
Mass of the planet

D
Distance of the planet from the sun

Solution

Kepler's first law provides information about the shape of the orbit

The correct option is (b)
Question 9
1 / -0

Under the influence of the Coulomb field of charge $$+Q$$, a charge $$-q$$ is moving it in an elliptical orbit. Find out the correct statement $$(s)$$.

A
The angular momentum of the charge $$-q$$ is constant

B
The linear momentum of the charge $$-q$$ is constant

C
The angular velocity of the charge $$-q$$ is constant

D
The linear speed of the charge $$-q$$ is constant

Solution

For a system of two charges under the action of centripetal and centrifugal forces, angular momentum remains concerned. This is the same as Kepler’s law of planetry motion.
Question 10
1 / -0

The acceleration due to gravity at a height $$\left (\dfrac {1}{20}\right )^{th}$$ the radius of earth above earth's surface is $$9\ m/s^{2}$$. Its value at a point at an equal distance below the surface of earth is ________ $$m/s^{2}$$.

A
$$55\ m/s^{2}$$

B
$$9.5\ m/s^{2}$$

C
$$12\ m/s^{2}$$

D
$$15\ m/s^{2}$$

Solution

The variation of acceleration due to gravity outside the earth.
$${ g }^{ 1 }=g\left( 1-\dfrac { 2h }{ R } \right) $$
$${ g }^{ 1 }=g\left( 1-\dfrac { 1 }{ 10 } \right) $$
$$g=g\left( \dfrac { 9 }{ 10 } \right) $$
$$g=10m/{ s }^{ 2 }$$
Now, for inside point,
$${ g }^{ 11 }=g\left( 1-\dfrac { d }{ R } \right) $$
$${ g }^{ 11 }=10\left( 1-\dfrac { 1 }{ 20 } \right) $$
$${ g }^{ 11 }=9.5m/{ s }^{ 2 }$$

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Gravitation Test - 52

Result

Gravitation Test - 52

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SHARING IS CARING

Question 1

planet moves in an hyperbolic path

planet moves in a parabolic path

planet moves in a straight line path

planet moves in a circular path

Solution

Question 2

work done in bringing an object from infinity to radius r

work done in moving an object around the earth

work done by an object in attaining an object's acceleration equal to $$9.8 m/s^2$$

work done in moving an object between two points horizontally

Solution

Question 3

Zero

W/4

W/2

W

Solution

Question 4

the product of force and velocity

the product of force and momentum

the product of weight and height lifted by an object

the product of force and displacement, if the particle is moving in a cirlce

Solution

Question 5

Potential of B is larger than potential of A

Objects starts moving in gravitational field until constant potential difference exist

The line B to A is equipotential surface

The mass moves from B to A, since A is nearer to origin

Solution

Question 6

$$6 kg-m^2/s$$

$$8 kg-m^2/s$$

$$4 kg-m^2/s$$

$$2 kg-m^2/s$$

Solution

Question 7

almost circular

almost elliptical

almost straight

parabolic

Solution

Question 8

areal velocity of a planet

Shape of the orbit of the planet

Mass of the planet

Distance of the planet from the sun

Solution

Question 9

The angular momentum of the charge $$-q$$ is constant

The linear momentum of the charge $$-q$$ is constant

The angular velocity of the charge $$-q$$ is constant

The linear speed of the charge $$-q$$ is constant

Solution

Question 10

$$55\ m/s^{2}$$

$$9.5\ m/s^{2}$$

$$12\ m/s^{2}$$

$$15\ m/s^{2}$$

Solution

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