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Heliocentric model - class-IX

Description: heliocentric model
Number of Questions: 56
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Tags: physics gravitation forces active without contact universe and space circular motion and gravitation
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What is the range of gravitational force. ?

  1. $10^{-2}$m

  2. $10^{-15}$m

  3. infinite

  4. $10^{-10}$m


Correct Option: C
Explanation:

The range of gravitational force is infinite.

Let $F _{1}$ be the magnitude of the gravitational force exerted on the Sun by Earth and $F _{2}$ be the magnitude of the force exerted on Earth by the Sun. Then.

  1. $F _{1}$ is much greater than $F _{2}$

  2. $F _{1}$ is slightly greater than $F _{2}$

  3. $F _{1}$ is equal to $F _{2}$

  4. $F _{1}$ is slightly less than $F _{2}$


Correct Option: C

Value of $G$ is

  1. $6.675\times {10}^{11}{Nm}^{2}{kg}^{-2}$

  2. $6.675\times {10}^{10}{Nm}^{2}{kg}^{-2}$

  3. $6.675\times {10}^{-12}{Nm}^{2}{kg}^{-2}$

  4. $6.675\times {10}^{-11}{Nm}^{2}{kg}^{-2}$


Correct Option: D

A block weights $5 N$ in air, $4.5 N$ in a liquid of specific gravity $0.5$ Its weight in water will be

  1. $3.5 N$

  2. $4.0 N$

  3. $2.5 N$

  4. $3.0 N$


Correct Option: A

------------ is the force of attraction between any two bodies in the universe.

  1. Gravitation

  2. Polarity

  3. Induction

  4. Joule


Correct Option: A
Explanation:

Any two objects attract each other with a force $F _g=\dfrac{GMm}{R^2}$ where $G$ is the gravitational constant, $M$ and $m$ the masses of the two bodies and $R$ is the distance along the line joining their centre of mass

State whether the given statement is True or False :

All objects attract each other along the line joining their centre of mass.

  1. True

  2. False


Correct Option: A
Explanation:

Any two objects attract each other with a force $F _g=\dfrac{GMm}{R^2}$ where $G$ is the gravitational constant, $M$ and $m$ the masses of the two bodies and $R$ is the distance along the line joining their centre of mass

The horizontal component of the weight of a body of mass $m$ is

  1. $mg$

  2. $\displaystyle \dfrac{\mathrm{m}\mathrm{g}}{2}$

  3. $0$

  4. Infinity


Correct Option: C
Explanation:

The force of gravity is the force with which the earth, moon, or other massively large object attracts another object towards itself. By definition, this is the weight of the object. All objects upon earth experience a force of gravity that is directed "downward" towards the center of the earth. So, the horizontal component of the weight of body of mass $m$ will be $0$. $Option$ $C$ is correct.

An Earth's satellite is moving in a circular orbit with a uniform speed $v$. If the gravitational force of the Earth suddenly disappears, the satellite will

  1. vanish into outer space.

  2. continue to move with velocity $v$ in original orbit.

  3. fall down with increasing velocity.

  4. fly off tangentially from the orbit with velocity $v$.


Correct Option: D
Explanation:

The satellite revolves around the Earth in a circular orbit when centrifugal force acting outward on the satellite is balanced by the gravitational force of the Earth. Thus, when gravitational force suddenly disappears, then only centrifugal force will be acting and velocity is tangential to the orbit and hence, the satellite will fly off tangentially. It is similar to an object tied with a string, fly off when string suddenly breaks.

The mass of the moon is about $1.2$% of the mass of the earth. Compared to the gravitational force the earth exerts on the moon, the gravitational force the moon exerts on earth

  1. Is the same

  2. Is smaller

  3. Is greater

  4. Varies with its phase


Correct Option: A
Explanation:

Answer is A.

By Newton's Third Law and Newton's Law of Universal gravitation, the gravitational force the Earth exerts on the Moon is exactly the same as the force the Moon exerts on the Earth. 
F (Earth) = F (Moon)
However, the tidal forces are not equal - the Moon exerts a greater tidal force because tidal forces result from a difference in force across the object. Because the Earth has a greater diameter, the difference in the lunar force across the Earth will be greater than the difference that the terrestrial force exerts across the lunar diameter.

When a fruit falls from a tree,

  1. only the earth attracts the fruit

  2. both the earth and the fruit attract each other

  3. only the fruit attracts the earth

  4. they repel each other


Correct Option: B
Explanation:

According to the law of physics, the earth attracts the apple and the apple attracts the earth with the same intensity of gravity ( according to 3rd law of dynamics). However the displacement of the two bodies is inversely to their respective masses. The earth attracts the apple i.e it falls on an apple in a billionth of a billionth of a millimeter which is impossible to see.

Thus when a fruit falls from a tree both the earth and the fruit attract each other.

The gravitational force is a

  1. contact force

  2. action at a distance force

  3. non contact force

  4. both (B) and (C)


Correct Option: D
Explanation:

Gravitational force is a action distance force because it can interact with an object even they are not in physical contact with each other, yet they are able to exert a push or a pull despite their physical operation. Hence gravitational force is a action at a distance force.

Gravitational force is also a non contact force because non contact force is a force which acts on an object without coming in physically contact with each other which is similar to a action at a distance force.

The weakest forces of interaction among all classified forces are

  1. electrostatic forces

  2. gravitational forces

  3. weak nuclear forces

  4. electromagnetic forces


Correct Option: B
Explanation:

Gravitational force is the weakest of all the forces because its coupling constant is small in value. Gravity cannot be felt in day to day life because of the huge universe surrounding earth. Electromagnetic force is the strongest of all  force as it deals with microscopic particles.

The gravitational force between two bodies is

  1. repulsive at large distances

  2. attractive at all places

  3. attractive at short distances

  4. repulsive at short distances


Correct Option: B
Explanation:

Gravitation is a natural phenomenon by which all things with mass are brought towards one another. It is an attractive force and behaves uniformly for all values of $r$ (distance between the two bodies).

On the surface of the earth, force of gravitational attraction between two masses kept at distance d apart is 6 Newtons. If these two masses are taken to the surface of the moon and kept at the same distance d, the force between them will be

  1. 1N

  2. 36N

  3. $\frac { 1 }{ 6 } $N

  4. 6N


Correct Option: D
Explanation:

Gravitational force by Newton's law must remain the same.


hence, $(D)$ is correct.

In SI unit gravitational unit of force is called 

  1. $Gf$

  2. $Kgf$

  3. $N$

  4. All


Correct Option: B
Explanation:

in SI system, gravitational unit of force is called kilogram force.

$1 gf =$

  1. $980 dyne$

  2. $98 dyne$

  3. $9.8 dyne$

  4. $0.98 dyne$



Correct Option: A
Explanation:

$1 gf = 1 g$ mass $\times$ acceleration due to gravity = $980 dyne$

$1 gf =$

  1. $250N$

  2. $980 dynes$

  3. $56 dynes$

  4. All


Correct Option: B
Explanation:

A force required to produce an acceleration due to gravity of earth in a body of mass 1g,is called gram force. $\displaystyle 1gm=1g\times 980c{ m }/{ { s }^{ 2 } }$ = 980 dynes.

One kilogramme force is the force due to gravity on a mass of

  1. $1 g$

  2. $10 g$

  3. $100 g$

  4. $1000 g$


Correct Option: D
Explanation:

One kilogramme force is the force due to gravity on a mass of $1 $kilogramme or $1000 g.$

In MKS, the gravitational unit of force is

  1. $kgf$

  2. $gf$

  3. $N$

  4. $dyne$


Correct Option: A
Explanation:

In MKS, the gravitational unit of force is kilogramme force (kgf).

In CGS, the gravitational unit of force is

  1. $kgf$

  2. $N$

  3. $gf$

  4. $dyne$


Correct Option: C
Explanation:

In CGS, the gravitational unit of force is gramme force ($gf$).

$1 g$ force is the force due to gravity on a mass of 

  1. $1 kg$

  2. $0.1 kg$

  3. $0.01 kg$

  4. $0.001 kg$


Correct Option: D
Explanation:

$1 g$ force is the force due to gravity on a mass of $1 g$ or $0.001 kg$.

A force which produces an acceleration in a body equal to acceleration due to gravity on earth, when the body has a unit mass is called

  1. Gravitational unit of force

  2. Gravity force

  3. Both

  4. None


Correct Option: A
Explanation:

Definition of gravitational unit of force: A force which produces an acceleration in a body equal to acceleration due to gravity on earth, when the body has a unit mass is called gravitational unit of force.

Gravitational unit of force produce an acceleration in a body equal to 

  1. $g$

  2. $0$

  3. $2g$

  4. unit value


Correct Option: A
Explanation:

Acceleration due to gravity is denoted by '$g$'.
A force which produces an acceleration in a body equal to acceleration due to gravity on earth, when the body has a unit mass is called gravitational unit of force.

State whether true or false.
The direction of the gravitational force is along the line joining the tips of the two bodies.
  1. True

  2. False


Correct Option: B
Explanation:

The direction of gravitational force is towards the line joining the body and the centre of the earth.


Hence the given statement is $False$ and correct option is $B$ 

State whether true or false.
The universal gravitational constant is independent of the intervening medium.
  1. True

  2. False


Correct Option: A
Explanation:

Gravity is unipolar, attractive. So when it goes through a medium, there is no polarizing effect or polarizing forces. Thus the gravitational constant is independent of the intervening medium.

If the gravitational force of earth suddenly disappears, then which of the following is correct?

  1. weight of the body is zero

  2. mass of the body is zero

  3. both mass and weight become zero

  4. neither the weight nor the mass is zero


Correct Option: A
Explanation:

Mass = $m$

Acceleration due to gravity = $g$
Weight of a body is given by, $(W) = m\times g$
When gravitational force disappears $g$ becomes zero, but the mass remains the same.
So, $W = m\times g=m\times 0$ 
Hence, $W = 0$
Correct option will be $(A)$

The orbit of the earth is an ellipse is an and not a circle. The distance between earth sun thus varies. On January 3, earth is closet to the sun (Perihelion). Similarly, earth is said to be at Aphelion, when it is farthest from the sun on ________.

  1. March, 23

  2. July, 4

  3. December, 23

  4. April, 21


Correct Option: B
Explanation:

Earth is about 147.1 million kilometres (91.4 million miles) from the Sun at perihelion around January 3, in contrast to about 152.1 million kilometres (94.5 million miles) at aphelion around July 4, a difference of about 5.0 million kilometres (3.1 million miles).

$1 kg wt$ is equal to

  1. $9.8 N$

  2. $980N$

  3. $98 N$

  4. none of these


Correct Option: A
Explanation:

1kgwt is equal to 9.8N.

$1 kg wt$ is equal to

  1. $980000 dynes$

  2. $9.80 dynes$

  3. $98 dynes$

  4. none of these


Correct Option: A
Explanation:

1kgwt = 9.8 N
1Newton = 100000 dynes
=> 1 kgwt = 980000 dynes

Two identical particles of mass m are placed at a distance r from each other. If their separation is doubled, then the effect on gravitational constant will be 

  1. Gravitational constant remains same

  2. Gravitational constant becomes quadrupled

  3. Gravitational constant becomes 1/4th the actual one

  4. Gravitational constant becomes doubled


Correct Option: A
Explanation:

Gravitational constant does not depend on masses, distances between them

Changing the distance between the masses, decreases the force between them, so that $Fr^2$ remains the same

The correct option is (a)

The gravitational force $F _{g}$ between two objects does not depend on

  1. sum of the masses

  2. product of mass

  3. graviational constant

  4. distance between the masses


Correct Option: A

The gravitational force between two points masses $m _{1}$ and $m _{2}$ at separation $r$ is given by $F=G\dfrac {m _{1}m _{2}}{r^{2}}$ The constant $G$

  1. depends on system of unit only

  2. depends on media between masses only

  3. depends on both $a$ and $b$

  4. is independent of both $a$ and $b$


Correct Option: D

At what height from the surface of the earth will the value of acceleration due to gravity be reduced by $36\%$ from the value at the surface?
(Radius of earth=$6400\ km$)

  1. $1500\ km$

  2. $1200\ km$

  3. $1000\ km$

  4. $1600\ km$


Correct Option: D

Two electrons are a certain distance apart from one another. What is the order of magnitude of the ratio of the electric force between them to the gravitational force between them?

  1. $10^8 : 1$

  2. $10^{28} : 1$

  3. $10^{31} : 1$

  4. $10^{42} : 1$


Correct Option: A

A cylinderical vessel is filled with equal amount of weight of mercury and water.The overall height of the two layer is 29.2 cm,specific gravity of mercury is 13.6.Then the pressure of the liquid at the bottom of the vessel is:

  1. $29.2 cm$ of water

  2. $\dfrac{29.2}{13.6} cm$ of mercury

  3. $4 cm$ of mercury

  4. $15.6 cm$ of mercury


Correct Option: C
Explanation:
${ M } _{ Hg }={ M } _{ w }$
${ P } _{ Hg }\left( A\times { L } _{ Hg } \right) ={ P } _{ w }\left( A\times { L } _{ w } \right) $
$\therefore$   ${ L } _{ w }=13.6{ L } _{ Hg }$
${ L } _{ w }+{ L } _{ Hg }=29.2$
$\Rightarrow { L } _{ Hg }=2cm\quad \quad { L } _{ w }=27.2cm=2cm$ of $Hg$
Total pressure $=4cm$ of $Hg$.

Two balls, each of radius $R$, equal mass and density are placed in contact, than the force of gravitation between them is proportional to

  1. $F\propto \dfrac {1}{R^{2}} $

  2. $F\propto R $

  3. $F\propto R^{4} $

  4. $F\propto \dfrac {1}{R} $


Correct Option: C
Explanation:
Given,

Two balls, each of radius $R$ and of equal mass and density, are placed in contact.

  • Step-1:

Find the Distance between the centre of two balls

Distance between the centre of two balls $=$ Sum of their Radii.

Distance between the centre of two balls $= R+R = 2R$.

  • Step-2:

Express the Mass of a ball as product of Density and Volume.

(This would be same for other ball ,given that two balls have equal mass)

Since, the shape of the ball is Sphere.

Volume of the ball $V=\dfrac 43 \pi R^3$

So,

Mass of the ball $m=\rho\times \dfrac 43 \pi R^3$

  • Step-3:

Find the force of gravitation between the two balls.

According to Newton's Law of Universal Gravitation

$F=\dfrac{GMm}{r^2}$

Where,

$F =$ Gravitational Force between two objects.

$G =$ Gravitational constant

$M =$ Mass of the first object

$m =$ Mass of the second object

$r =$ Distance between objects

Here,
.
$M=m=\rho \times \dfrac 43 \pi R^3$

Substituting Values

$\implies F=\dfrac{Gm^2}{(2R)^2}$

$\implies F=\dfrac{G(\rho \times \dfrac 43\pi R^3)^2}{4R^2}$

$\implies F=G\times \rho^2\times (\dfrac 43)^2 \times \dfrac 14\times \dfrac{R^6}{R^2}$

$\implies F=G\times \rho^2\times (\dfrac 43)^2 \times \dfrac 14 \times R^4$

$\implies F\propto R^4$

Therefore,

The force of gravitation between the two balls is proportional to $R^4$

A satellite of the earth is revolving in circular orbit with a uniform velocity V. If the gravitational force suddenly disappears, the satellite will

  1. continue to move with the same velocity in the same orbit.

  2. move tangentially to the original orbit with velocity V.

  3. fall down with increasing velocity.

  4. come to a stop somewhere in its original orbit.


Correct Option: B
Explanation:

The satellite is revolving around earth because the centripetal force is balanced by earth's gravitational pull.If the gravitational pull disappears, the satellite free of centripetal force. So, it will travel with its instantaneous velocity i.e. in the direction tangential to the circular path.

The gravitational force on a body of mass $5\ kg$ at the surface of the earth is $50\ N$. If earth is a perfect sphere, the gravitational force on a satellite of ass $200\ kg$ in a circuit orbit of radius same as diameter of the earth is.

  1. $200\ N$

  2. $400\ N$

  3. $500\ N$

  4. $800\ N$


Correct Option: A

A body has a weight $90\ N$ on the earth's surface the mass of the moon is $1/9$ that of the earth's mass and its radius is $1/2$ that of the earth's radius. on the moon the weight of the body is :

  1. $45\ N$

  2. $202.5\ N$`

  3. $90\ N$

  4. $40\ N$


Correct Option: D

If the distance between two bodies is doubles, the force of gravitational attraction between them. 

  1. Becomes four times

  2. Is doubled

  3. Is reduced to one-fourth

  4. Is reduced to half.


Correct Option: C

Two solid spherical planets of equal radii R having masses 4 M and 9 M their centre are separated by a distance 6 R. A projectile of mass m is sent from the planet of mass 4 M towards the havier planet. what is the distance r of the point from the lighter planet where the gravitational force on the projectile is zero? 

  1. $1.4 R$

  2. $1.8 R$

  3. $1.5 R$

  4. $2.4 R$


Correct Option: D

If an orbiting satellite comes to a standstill suddenly,

  1. the satellite will move along the tangent.

  2. the satellite will move radically towards centre of the orbit.

  3. the satellite will go to outer space and will be lost.

  4. the satellite will continue to move in the same orbit.


Correct Option: B
Explanation:

If the satellite is brought to standstill $v=0$ which gives the net force on the satellite=
$F=\dfrac{GMm}{{a}^{2}} $ in the direction of the centre of the earth which earlier was providing centripetal acceleration. So the satellite will fall on the earth

The moon revolves round the earth  $13$  times in one year. If the ratio of sun-earth distance to earth-moon distance is  $392,$  then the ratio of masses of sun and earth will be

  1. $365$

  2. $356 \times 10 ^ { - 12 }$

  3. $3.56 \times 10 ^ { 5 }$

  4. $1$


Correct Option: C

Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F$. The space around the masses is now filled with a liquid of specific gravity $3$. The gravitational force will now be

  1. $2 F$

  2. $F$

  3. $\displaystyle\frac {F}{3}$

  4. $\displaystyle \frac {F}{9}$


Correct Option: B
Explanation:

The force of gravitation will be same as $F$ because gravitational force is dependent on the masses of the body and distance between them and does not depend on the medium between the masses.

The force acting on a mass of 1g due to the gravitational pull on the earth is called 1gwt. One gwt equals:

  1. 1 N

  2. 9.8 N

  3. 980 dyne

  4. none of these


Correct Option: C
Explanation:

1gwt is the force acting on a mass of $1g$ due to gravitational pull on earth

$1gwt=\frac{1}{1000}Kg \times 9.8ms^{-2}$
             =$9.8\times 10^{-3}N$
$1N=10^{5}dyne$
$9.8\times 10^{-3}N=980dyne$

$1gwt=980 dyne$

The motion of planets in the solar system is an exampIe of the conservation of

  1. mass

  2. linear momentum

  3. angular momentum

  4. energy


Correct Option: C
Explanation:

For any circular motion the angular momentum is conserved as no torque is acting on it because centripetal force acts through the point of axis.

$1 kgf =$

  1. $1 gf$

  2. $10 gf$

  3. $100 gf$

  4. $1000 gf$


Correct Option: D
Explanation:

$1 kgf = 9.8 N =9.8 \times {10}^{5}dyne=980 \ times 1000 dyne=1000 \times (980dyne)=1000gf$

The gravitational force with which the earth attracts the moon :

  1. is less than the force with which the moon attracts the earth

  2. is equal to the force with which the moon attracts the earth

  3. is greater than the force with which the moon attracts the earth

  4. varies with the phases of the moon


Correct Option: B
Explanation:

By the Newton's gravitational law, the gravitational force between two bodies of masses $m _1$ and $m _2$ is given by $F=-\dfrac{Gm _1m _2}{r^2}$

where $r$ be the distance between them and negative sign indicates the attraction force. 
Thus, both of them attract each other with same force.

State whether true or false.
Gravitational forces can also be repulsive like that of electrostatic forces.
  1. True

  2. False


Correct Option: B
Explanation:

Gravitational force, $F=\cfrac { G{ M } _{ 1 }{ M } _{ 2 } }{ { R }^{ 2 } } $

Now the mass of the objects can not be opposite (i.e., mass cannot be negative), thus, the nature of the force cannot be repulsive like that of electrostatic force.

The mass of the moon is about $1.2$% of the mass of the earth. Compared to the gravitational force that earth exerts on the moon, the gravitational force the moon exerts on earth :

  1. is the same

  2. is smaller

  3. is greater

  4. Varies with its plane


Correct Option: A
Explanation:

The gravitation force of attraction between two bodies is given by, $F=-\dfrac{Gm _1m _2}{r^2}$ where $G=$ gravitational constant, $m _1,m _2$  be the masses of bodies and $r$ be the distance between them.

As the force depends on the product of masses and distance between them, so same force will exert on each other.

If E, M, J and G, respectively, denote energy, mass, angular momentum, and gravitational constant, then $EJ^2 / M^5G^2$ has the dimensions of

  1. Time

  2. Angle

  3. Mass

  4. Length


Correct Option: B
Explanation:

$E=ML^2T^{-2}\ M+ML^0T^0\ G=M^{-1}L^3T^{-2}\ J=ML^2T^{-1}$

$EJ^2/M^5G^2=Ml^2T^{-2}\times M^2L^2T^{-1}$
$=M^5\times M^{-2}\times L^{-6}T^{-4}\ =M^0L^0T^0$

Choose the correct statement:

  1. The dimensional formula for $G$ is ${M}^{-1}{L}^{3}{T}^{-2}$

  2. $G$ is independent of medium

  3. $F=G\cfrac{{m} _{1}{m} _{2}}{{r}^{2}}$

  4. All of the above


Correct Option: D

To double the orbital speed V and halve the angular velocity $\omega $, The centripetal acceleration of a revolving body:

  1. Is quadrupled

  2. Remains Unchanged

  3. Is halved

  4. Is doubled


Correct Option: A

The force of attraction between two unit point masses separated by a unit distance is called

  1. Gravitational potential

  2. Acceleration due to gravity.

  3. Gravitational field

  4. Universal gravitational constant.


Correct Option: D
Explanation:

Universal gravitational constant is the force of attraction between two bodies of unit mass and at a unit distance from each other.

In the relation F= $\dfrac{G M m}{r^{2}}$, the quantity G

  1. depends on the value of g at the place of observation.

  2. is used only when the earth is one of the two masses.

  3. is greatest at the surface of the earth.

  4. is universal constant in nature.


Correct Option: D
Explanation:

G is the universal gravitational constant which remains constant irrespective of the place and time. G is the force of attraction between two bodies of unit mass and unit distance apart.

A body of mass $5\ kg$ is cut into two parts of masses (a) $\dfrac {m}{4}; \dfrac {3m}{4}$ (b) $\dfrac {m}{7}; \dfrac {5m}{7}$ (c) $\dfrac {m}{2}; \dfrac {m}{2}$ (d) $\dfrac {m}{5}; \dfrac {4m}{5}$. When these two pieces are kept apart by certain distance; In which case the gravitational force acting is maximum?

  1. In case a

  2. In case C

  3. In case d

  4. In case b


Correct Option: B
Explanation:

Gravitation force between two masses is given by $F=\cfrac { G{ m } _{ 1 }{ m } _{ 2 } }{ { r }^{ 2 } } $

In case I:${ F } _{ 1 }=\cfrac { G\cfrac { m }{ 4 } .\cfrac { 3m }{ 4 }  }{ { r }^{ 2 } } =\cfrac { G{ m }^{ 2 } }{ { r }^{ 2 } } \times \cfrac { 1 }{ 16 } =\cfrac { G{ m }^{ 2 } }{ { r }^{ 2 } } \times 0.0625$
In case II: ${ F } _{ 2 }=\cfrac { G\cfrac { m }{ 7 } .\cfrac { 5m }{ 7 }  }{ { r }^{ 2 } } =\cfrac { G{ m }^{ 2 } }{ { r }^{ 2 } } \times \cfrac { 5 }{ 7 } =\cfrac { G{ m }^{ 2 } }{ { r }^{ 2 } } \times 0.714$
In case III: ${ F } _{ 3 }=\cfrac { G\cfrac { m }{ 2 } .\cfrac { m }{ 2 }  }{ { r }^{ 2 } } =\cfrac { G{ m }^{ 2 } }{ { r }^{ 2 } } .\cfrac { 1 }{ 4 } =\cfrac { G{ m }^{ 2 } }{ { r }^{ 2 } } \times 0.25$
${ F } _{ 2 }$ is maximum.

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