QBManager

Gravitation

138331 The earth is assumed to be a sphere of radius (R) rotating about its axis with an angular speed $ω$ . If the effective acceleration due to gravity at a certain latitude $λ$ is $g_{p} - \frac{3}{4} ω^{2} R$ , where $g_{p}$ is the acceleration due to gravity at the poles, then the value of $λ$ is

1

45^{\circ}

2

30^{\circ}

3

90^{\circ}

4

90^{\circ}

Explanation:

B
Given,
The effective acceleration due to gravity at a certain latitude $(λ)$ ,
$g^{'} = g - R ω^{2} \cos^{2} λ$
at pole, $λ = 90^{\circ}$
$g_{p} = g - R ω^{2} \cos^{2} 90^{\circ}$
$g_{P} = g - 0$
$g_{P} = g$ , thus, it will be same.
Putting the value of $g$ in equation (i),
$g^{'} = g_{P} - R ω^{2} \cos^{2} λ$
$g^{'} = g_{P} - \frac{3}{4} ω^{2} R$ (given)
...(iii)
On comparing eq $^{n}$ (ii) and (iii) we get,
$\cos^{2} λ = \frac{3}{4}$
$\cos λ = \frac{\sqrt{3}}{2} = \cos 30^{\circ}$
$λ = 30^{\circ}$

COMEDK 2019

Gravitation

138332 Assertion: If earth suddenly stops rotating about its axis, then the value of acceleration due to gravity will become same at all the places.
Reason: The value of acceleration due to gravity depends upon the rotation of the earth.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

3 If Assertion is correct but Reason is incorrect.

4 If both the Assertion and Reason are incorrect.

Explanation:

A
$g^{'} = g - ω^{2} R_{e} \cos^{2} λ$
$ω =$ angular velocity of the earth
$F_{c} =$ centrifugal force
According to assertion if earth stops rotating then velocity $(ω)$ becomes zero and thus $g^{'} = g$ . Hence the assertion is correct.
We have seen equation (i) acceleration due to gravity is not dependent on the rotation of earth so the reason is also correct.

AIIMS-27.05.2018(E)

Gravitation

138333 Assertion: Space rocket are usually launched in the equatorial line from west to east.
Reason: The acceleration due to gravity is minimum at the equator.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

3 If Assertion is correct but Reason is incorrect.

4 If both the Assertion and Reason are incorrect.

Explanation:

B As we know that our earth rotates from west to east so when a rocket is propelled from west to east in the equatorial plane. Therefore all the particles on the earth have velocity from west to east. This velocity is maximum in the equatorial line. as, $V = R ω$
Where, $R =$ the radius of earth
and $ω =$ the angular velocity of revolution of earth about its polar axis.
When a rocket is launched from west to east in equatorial plane the maximum linear velocity is added to the launching velocity of the rocket due to which launching becomes easier.
Also, $g^{'} = g - ω^{2} R \cos^{2} λ$
At equator, $λ = 0^{\circ}$
$g^{'} = g - ω^{2} R \cos^{2} 0^{\circ}$
$g^{'} = g - ω^{2} R$
$g^{'}$ is least at equator
So, both assertion and reason are correct but reason is not correct explanation of assertion.

AIIMS-2017

Gravitation

138334 Assertion: An astronaut experience weightlessness in a space satellite.
Reason: When a body falls freely it does not experience gravity.

1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.

3 If the Assertion is correct but Reason is incorrect.

4 If both the Assertion and Reason are incorrect.

5 If the Assertion is incorrect but the Reason is correct.

AIIMS-2007

Gravitation

138331 The earth is assumed to be a sphere of radius (R) rotating about its axis with an angular speed $ω$ . If the effective acceleration due to gravity at a certain latitude $λ$ is $g_{p} - \frac{3}{4} ω^{2} R$ , where $g_{p}$ is the acceleration due to gravity at the poles, then the value of $λ$ is

1

45^{\circ}

2

30^{\circ}

3

90^{\circ}

4

90^{\circ}

Explanation:

B
Given,
The effective acceleration due to gravity at a certain latitude $(λ)$ ,
$g^{'} = g - R ω^{2} \cos^{2} λ$
at pole, $λ = 90^{\circ}$
$g_{p} = g - R ω^{2} \cos^{2} 90^{\circ}$
$g_{P} = g - 0$
$g_{P} = g$ , thus, it will be same.
Putting the value of $g$ in equation (i),
$g^{'} = g_{P} - R ω^{2} \cos^{2} λ$
$g^{'} = g_{P} - \frac{3}{4} ω^{2} R$ (given)
...(iii)
On comparing eq $^{n}$ (ii) and (iii) we get,
$\cos^{2} λ = \frac{3}{4}$
$\cos λ = \frac{\sqrt{3}}{2} = \cos 30^{\circ}$
$λ = 30^{\circ}$

COMEDK 2019

Gravitation

138332 Assertion: If earth suddenly stops rotating about its axis, then the value of acceleration due to gravity will become same at all the places.
Reason: The value of acceleration due to gravity depends upon the rotation of the earth.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

3 If Assertion is correct but Reason is incorrect.

4 If both the Assertion and Reason are incorrect.

Explanation:

A
$g^{'} = g - ω^{2} R_{e} \cos^{2} λ$
$ω =$ angular velocity of the earth
$F_{c} =$ centrifugal force
According to assertion if earth stops rotating then velocity $(ω)$ becomes zero and thus $g^{'} = g$ . Hence the assertion is correct.
We have seen equation (i) acceleration due to gravity is not dependent on the rotation of earth so the reason is also correct.

AIIMS-27.05.2018(E)

Gravitation

138333 Assertion: Space rocket are usually launched in the equatorial line from west to east.
Reason: The acceleration due to gravity is minimum at the equator.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

3 If Assertion is correct but Reason is incorrect.

4 If both the Assertion and Reason are incorrect.

Explanation:

B As we know that our earth rotates from west to east so when a rocket is propelled from west to east in the equatorial plane. Therefore all the particles on the earth have velocity from west to east. This velocity is maximum in the equatorial line. as, $V = R ω$
Where, $R =$ the radius of earth
and $ω =$ the angular velocity of revolution of earth about its polar axis.
When a rocket is launched from west to east in equatorial plane the maximum linear velocity is added to the launching velocity of the rocket due to which launching becomes easier.
Also, $g^{'} = g - ω^{2} R \cos^{2} λ$
At equator, $λ = 0^{\circ}$
$g^{'} = g - ω^{2} R \cos^{2} 0^{\circ}$
$g^{'} = g - ω^{2} R$
$g^{'}$ is least at equator
So, both assertion and reason are correct but reason is not correct explanation of assertion.

AIIMS-2017

Gravitation

138334 Assertion: An astronaut experience weightlessness in a space satellite.
Reason: When a body falls freely it does not experience gravity.

1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.

3 If the Assertion is correct but Reason is incorrect.

4 If both the Assertion and Reason are incorrect.

5 If the Assertion is incorrect but the Reason is correct.

AIIMS-2007

Gravitation

138331 The earth is assumed to be a sphere of radius (R) rotating about its axis with an angular speed $ω$ . If the effective acceleration due to gravity at a certain latitude $λ$ is $g_{p} - \frac{3}{4} ω^{2} R$ , where $g_{p}$ is the acceleration due to gravity at the poles, then the value of $λ$ is

1

45^{\circ}

2

30^{\circ}

3

90^{\circ}

4

90^{\circ}

Explanation:

B
Given,
The effective acceleration due to gravity at a certain latitude $(λ)$ ,
$g^{'} = g - R ω^{2} \cos^{2} λ$
at pole, $λ = 90^{\circ}$
$g_{p} = g - R ω^{2} \cos^{2} 90^{\circ}$
$g_{P} = g - 0$
$g_{P} = g$ , thus, it will be same.
Putting the value of $g$ in equation (i),
$g^{'} = g_{P} - R ω^{2} \cos^{2} λ$
$g^{'} = g_{P} - \frac{3}{4} ω^{2} R$ (given)
...(iii)
On comparing eq $^{n}$ (ii) and (iii) we get,
$\cos^{2} λ = \frac{3}{4}$
$\cos λ = \frac{\sqrt{3}}{2} = \cos 30^{\circ}$
$λ = 30^{\circ}$

COMEDK 2019

Gravitation

138332 Assertion: If earth suddenly stops rotating about its axis, then the value of acceleration due to gravity will become same at all the places.
Reason: The value of acceleration due to gravity depends upon the rotation of the earth.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

3 If Assertion is correct but Reason is incorrect.

4 If both the Assertion and Reason are incorrect.

Explanation:

A
$g^{'} = g - ω^{2} R_{e} \cos^{2} λ$
$ω =$ angular velocity of the earth
$F_{c} =$ centrifugal force
According to assertion if earth stops rotating then velocity $(ω)$ becomes zero and thus $g^{'} = g$ . Hence the assertion is correct.
We have seen equation (i) acceleration due to gravity is not dependent on the rotation of earth so the reason is also correct.

AIIMS-27.05.2018(E)

Gravitation

138333 Assertion: Space rocket are usually launched in the equatorial line from west to east.
Reason: The acceleration due to gravity is minimum at the equator.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

3 If Assertion is correct but Reason is incorrect.

4 If both the Assertion and Reason are incorrect.

Explanation:

B As we know that our earth rotates from west to east so when a rocket is propelled from west to east in the equatorial plane. Therefore all the particles on the earth have velocity from west to east. This velocity is maximum in the equatorial line. as, $V = R ω$
Where, $R =$ the radius of earth
and $ω =$ the angular velocity of revolution of earth about its polar axis.
When a rocket is launched from west to east in equatorial plane the maximum linear velocity is added to the launching velocity of the rocket due to which launching becomes easier.
Also, $g^{'} = g - ω^{2} R \cos^{2} λ$
At equator, $λ = 0^{\circ}$
$g^{'} = g - ω^{2} R \cos^{2} 0^{\circ}$
$g^{'} = g - ω^{2} R$
$g^{'}$ is least at equator
So, both assertion and reason are correct but reason is not correct explanation of assertion.

AIIMS-2017

Gravitation

138334 Assertion: An astronaut experience weightlessness in a space satellite.
Reason: When a body falls freely it does not experience gravity.

1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.

3 If the Assertion is correct but Reason is incorrect.

4 If both the Assertion and Reason are incorrect.

5 If the Assertion is incorrect but the Reason is correct.

AIIMS-2007

Gravitation

138331 The earth is assumed to be a sphere of radius (R) rotating about its axis with an angular speed $ω$ . If the effective acceleration due to gravity at a certain latitude $λ$ is $g_{p} - \frac{3}{4} ω^{2} R$ , where $g_{p}$ is the acceleration due to gravity at the poles, then the value of $λ$ is

1

45^{\circ}

2

30^{\circ}

3

90^{\circ}

4

90^{\circ}

Explanation:

B
Given,
The effective acceleration due to gravity at a certain latitude $(λ)$ ,
$g^{'} = g - R ω^{2} \cos^{2} λ$
at pole, $λ = 90^{\circ}$
$g_{p} = g - R ω^{2} \cos^{2} 90^{\circ}$
$g_{P} = g - 0$
$g_{P} = g$ , thus, it will be same.
Putting the value of $g$ in equation (i),
$g^{'} = g_{P} - R ω^{2} \cos^{2} λ$
$g^{'} = g_{P} - \frac{3}{4} ω^{2} R$ (given)
...(iii)
On comparing eq $^{n}$ (ii) and (iii) we get,
$\cos^{2} λ = \frac{3}{4}$
$\cos λ = \frac{\sqrt{3}}{2} = \cos 30^{\circ}$
$λ = 30^{\circ}$

COMEDK 2019

Gravitation

138332 Assertion: If earth suddenly stops rotating about its axis, then the value of acceleration due to gravity will become same at all the places.
Reason: The value of acceleration due to gravity depends upon the rotation of the earth.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

3 If Assertion is correct but Reason is incorrect.

4 If both the Assertion and Reason are incorrect.

Explanation:

A
$g^{'} = g - ω^{2} R_{e} \cos^{2} λ$
$ω =$ angular velocity of the earth
$F_{c} =$ centrifugal force
According to assertion if earth stops rotating then velocity $(ω)$ becomes zero and thus $g^{'} = g$ . Hence the assertion is correct.
We have seen equation (i) acceleration due to gravity is not dependent on the rotation of earth so the reason is also correct.

AIIMS-27.05.2018(E)

Gravitation

138333 Assertion: Space rocket are usually launched in the equatorial line from west to east.
Reason: The acceleration due to gravity is minimum at the equator.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

3 If Assertion is correct but Reason is incorrect.

4 If both the Assertion and Reason are incorrect.

Explanation:

B As we know that our earth rotates from west to east so when a rocket is propelled from west to east in the equatorial plane. Therefore all the particles on the earth have velocity from west to east. This velocity is maximum in the equatorial line. as, $V = R ω$
Where, $R =$ the radius of earth
and $ω =$ the angular velocity of revolution of earth about its polar axis.
When a rocket is launched from west to east in equatorial plane the maximum linear velocity is added to the launching velocity of the rocket due to which launching becomes easier.
Also, $g^{'} = g - ω^{2} R \cos^{2} λ$
At equator, $λ = 0^{\circ}$
$g^{'} = g - ω^{2} R \cos^{2} 0^{\circ}$
$g^{'} = g - ω^{2} R$
$g^{'}$ is least at equator
So, both assertion and reason are correct but reason is not correct explanation of assertion.

AIIMS-2017

Gravitation

138334 Assertion: An astronaut experience weightlessness in a space satellite.
Reason: When a body falls freely it does not experience gravity.

1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.

3 If the Assertion is correct but Reason is incorrect.

4 If both the Assertion and Reason are incorrect.

5 If the Assertion is incorrect but the Reason is correct.

AIIMS-2007

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