Gravitation Test

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Gravitation Test - 20

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Question 1
1 / -0

Escape velocity of a particle depends on its mass m as

A
$$m^2$$

B
$$m$$

C
$$m^0$$

D
$$m^{_1}$$

Solution

Escape velocity,
$$v_e=\sqrt{2gR}$$
it is independent of the mass of the particle.
Thus it will depend on $$m^0$$.
hence, option C is correct.
Question 2
1 / -0

The scientist who gave me three laws of planetary motion was

A
Newton

B
Kepler

C
Galileo

D
Robert Boyle
Solution
Answer is B.

In the early 1600s, Johannes Kepler proposed three laws of planetary motion.
Kepler's three laws of planetary motion can be described as follows:
- The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)
- An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas)
- The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies)
Question 3
1 / -0

The value of gravitational acceleration g at the center of the earth is:-

A
Infinite

B
$$\displaystyle 9.8{ m }/{ { s }^{ 2 } }$$

C
$$\displaystyle 32.2{ m }/{ { s }^{ 2 } }$$

D
Zero

Solution

acceleration due to gravity varies directly proportional to distance from center, i.e. r<R.
But varies $$\dfrac{1}{r^2}$$ when r>R
expression is given by $$g=\dfrac{GM}{r^2}$$ if r>R.
and $$g=\dfrac{GMr}{R^3}$$ if r<R

so when $$r=0$$ then g will be zero.
Question 4
1 / -0

The value of '$$g$$' is zero

A
At the top atmosphere

B
At $$20 km$$ below the surface of the earth

C
At $$20 km$$ above the surface of the earth

D
At the centre of the earth

Solution

At the center, for every particle of mass in the earth to attract you gravitationally, there's an equal particle with the same mass, located at the same distance from you in exactly the opposite direction, balancing out the force toward the first one. All of this is a theoretically ideal case. It assumes that the earth is a perfect sphere, with the same distribution of mass in every direction from the center.so, the acceleration of gravity would be zero at the center.
hence,option D is correct.
Question 5
1 / -0

The ratio of the value of G in SI units to CGS units is

A
$$10^3:1$$

B
$$10^2:1$$

C
$$10^{-2}:1$$

D
$$10^{-3}:1$$

Solution

$$\text{Quantity}$$ $$\text{SI System}$$ $$\text{CGS System}$$
Force Newton (N) dyne
Distance metre (m) centi-meter (cm)
Mass kilogram (kg) gram (g)
The unit of G can be calculated by putting the unit of all the quantities in the expression of the force due to gravity.
$$\dfrac{Gm_1m_2}{r^2}=F$$ $$\Rightarrow G=\dfrac{F\times r^2}{m_1\times m_2}$$

So we get, $$\text{Unit of G}=\dfrac{\text{Unit of force}\times \text{(Unit of distance)}^2}{\text{(Unit of mass)}^2}$$

$$\text{SI unit of G}=\dfrac{N.m^2}{kg^2}$$ and $$\text{CGS unit of G}=\dfrac{dyne.cm^2}{g^2}$$

We know that $$1\ N = 10^5\ dyne$$, $$1\ kg = 10^3\ g$$ and $$1\ m = 10^2\ cm$$

$$\underline{\text{Required ratio:}}$$
$$\dfrac{SI}{CGS}=\dfrac{N.m^2.g^{-2}}{dyne.cm^2.kg^{-2}}=\dfrac{10^{5}\ dyne\times 10^4\ cm^2\times g^{-2}}{dyne\times cm^2\times 10^{-6}\ g^{-2}}=10^3 : 1$$

So the answer is option A.
Question 6
1 / -0

The value of G depends on

A
the nature of the interacting bodies

B
the size of the interacting bodies

C
the mass of the interacting bodies

D
none of these

Solution

G is symbol used for gravitational constant, it is a universal constant and independent from type, place, mass, density, volume everything.
it is always constant.
so option D is the answer.
Question 7
1 / -0

In a vacuum on the earth surface, all freely falling bodies

A
have the same speed

B
have the same velocity

C
have the same force

D
have the same acceleration

Solution

a force acting on the body is given by $$F=\dfrac{GMm}{r^2}$$
here $$m$$ is different for different bodies hence force acting on different bodies will be different.
acceleration is $$\dfrac{force}{mass}=\dfrac{GM}{r^2}$$, this is independent of the mass of the body or type of the body.
also, speed or velocity depends on time for which it is accelerated because acceleration is the same.
hence correct option is D.
Question 8
1 / -0

The value of $$g$$

A
Decreases with height from earth's surface

B
Increases with height from earth's surface

C
Remain unchanged with increase of height from earth's surface

D
None of these

Solution

$$g_h=g(1-\cfrac{2h}{r})$$
So, The value of acceleration due to gravity decreases with increase in height above the surface of the earth.
hence,option A is correct.
Question 9
1 / -0

At the centre of the earth, the value of g becomes

A
zero

B
unity

C
infinity

D
none of these

Solution

acceleration due to gravity varies directly proportional to distance from center, i.e. r<R.
But varies $$\dfrac{1}{r^2}$$ when r>R
expression is given by $$g=\dfrac{GM}{r^2}$$ if r>R.
and $$g=\dfrac{GMr}{R^3}$$ if r<R

so when $$r=0$$ then g will be zero.
so the answer is option A.
Question 10
1 / -0

Asteroids are

A
A group of small heavenly bodies, forming a belt rotating round the sun

B
Starts forming a recognizable pattern

C
Solid bodies from the outer space

D
A large cluster of stars distributed in the universe in an irregular form

Solution

Asteriods are the minor planets that revolve around the sun in inner solar system forming eccentric orbits.
Option A is correct.

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$$\text{Quantity}$$	$$\text{SI System}$$	$$\text{CGS System}$$
Force	Newton (N)	dyne
Distance	metre (m)	centi-meter (cm)
Mass	kilogram (kg)	gram (g)

Gravitation Test - 20

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Gravitation Test - 20

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Question 1

$$m^2$$

$$m$$

$$m^0$$

$$m^{_1}$$

Solution

Question 2

Newton

Kepler

Galileo

Robert Boyle

Solution

Question 3

Infinite

$$\displaystyle 9.8{ m }/{ { s }^{ 2 } }$$

$$\displaystyle 32.2{ m }/{ { s }^{ 2 } }$$

Zero

Solution

Question 4

At the top atmosphere

At $$20 km$$ below the surface of the earth

At $$20 km$$ above the surface of the earth

At the centre of the earth

Solution

Question 5

$$10^3:1$$

$$10^2:1$$

$$10^{-2}:1$$

$$10^{-3}:1$$

Solution

Question 6

the nature of the interacting bodies

the size of the interacting bodies

the mass of the interacting bodies

none of these

Solution

Question 7

have the same speed

have the same velocity

have the same force

have the same acceleration

Solution

Question 8

Decreases with height from earth's surface

Increases with height from earth's surface

Remain unchanged with increase of height from earth's surface

None of these

Solution

Question 9

zero

unity

infinity

none of these

Solution

Question 10

A group of small heavenly bodies, forming a belt rotating round the sun

Starts forming a recognizable pattern

Solid bodies from the outer space

A large cluster of stars distributed in the universe in an irregular form

Solution

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