359623
Assertion : Space rockets are usually launched in the equatorial line from west to east. Reason : The acceleration due to gravity is minimum at the equator.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Earth's rotation is taking place from west to east. Earth's eastward rotation imparts a maximum velocity at the equator, aiding rockets launched west to east. This effect eases the launch process due to the added linear velocity from Earth's rotation. Reason is separate fact. So correct option is (2).
PHXI08:GRAVITATION
359624
\(T\) is the time period of simple pendulum on the earth's surface. Its time period becomes \(x T\) when taken to a height \(R\) (equal to earth's radius) above the earth's surface. Then, the value of \(x\) will be
1 \(\dfrac{1}{2}\)
2 4
3 \(\dfrac{1}{4}\)
4 2
Explanation:
Time period on earth's surface \(=T\), Height, \(h=R\) Let the new period is \(T^{\prime}\). At height \(h=R\), value of \(g\) becomes \(g^{\prime}\) \(g^{\prime}=g\left(\dfrac{R}{R+h}\right)^{2}=g\left(\dfrac{R}{R+R}\right)^{2}=\dfrac{g}{4}\) As, time period, \(T \propto \dfrac{1}{\sqrt{g}} \quad\left(\because T=2 \pi \sqrt{\dfrac{l}{g}}\right)\) \(\dfrac{T^{\prime}}{T}=\sqrt{\dfrac{g}{g^{\prime}}}=\sqrt{\dfrac{g}{g} \times 4}=2\) \(T^{\prime}=2 T\) So, \(x=2\)
JEE - 2023
PHXI08:GRAVITATION
359625
Assertion : If a pendulum is suspended in a lift and lift falling freely, then its time period becomes infinite. Reason : Free falling body has acceleration equal to acceleration due to gravity.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The pendulum's time period (T) in a descending elevator is calculated by \(T=2 \pi \sqrt{\dfrac{l}{g-a}}\), where 'l' is length, ' \(g\) ' is gravity, and ' \(\mathrm{a}\) ' is elevator acceleration. In free fall \((a=\) \(g\) ), \(\mathrm{T}\) becomes infinite, leading to an indefinitely long pendulum period. So correct option is (1)
PHXI08:GRAVITATION
359626
Assertion : There is no effect (felt) of rotation of earth on acceleration due to gravity at poles. Reason : Rotation of earth is about polar axis.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rotation (with \(\omega\) ) of the Earth about its axis does not affect the acceleration due to gravity at the poles. At poles \(\lambda=90^{\circ}\) \(\Rightarrow \cos \lambda=0\) \(\Rightarrow g^{\prime}=g\) Body at poles does not feel centrifugal force. The direction of rotation is perpendicular to the force of gravity. So correct option is (1).
PHXI08:GRAVITATION
359627
Match the Column I with Column II. Column I Column II A Weight P Minimum B \({{\rm{g}}_{{\rm{equator}}}}\) Q Zero C \({{\text{g}}_{{\text{poles}}}}\) R Vector D \({{\text{g}}_{{\text{center}}}}\) S Maximum
1 A - Q, B - P, C - R, D - S
2 A - Q, B - Q, C - S, D - R
3 A - R, B - P, C - S, D - Q
4 A - S, B - R, C - P, D - Q
Explanation:
Weight is a vector quantity. The effective acceleration due to gravity is maximum at poles since centrifugal force is zero . There similary \(g\) at equal for is minimum as centrifugal force is maximum there. option (3) is correct.
359623
Assertion : Space rockets are usually launched in the equatorial line from west to east. Reason : The acceleration due to gravity is minimum at the equator.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Earth's rotation is taking place from west to east. Earth's eastward rotation imparts a maximum velocity at the equator, aiding rockets launched west to east. This effect eases the launch process due to the added linear velocity from Earth's rotation. Reason is separate fact. So correct option is (2).
PHXI08:GRAVITATION
359624
\(T\) is the time period of simple pendulum on the earth's surface. Its time period becomes \(x T\) when taken to a height \(R\) (equal to earth's radius) above the earth's surface. Then, the value of \(x\) will be
1 \(\dfrac{1}{2}\)
2 4
3 \(\dfrac{1}{4}\)
4 2
Explanation:
Time period on earth's surface \(=T\), Height, \(h=R\) Let the new period is \(T^{\prime}\). At height \(h=R\), value of \(g\) becomes \(g^{\prime}\) \(g^{\prime}=g\left(\dfrac{R}{R+h}\right)^{2}=g\left(\dfrac{R}{R+R}\right)^{2}=\dfrac{g}{4}\) As, time period, \(T \propto \dfrac{1}{\sqrt{g}} \quad\left(\because T=2 \pi \sqrt{\dfrac{l}{g}}\right)\) \(\dfrac{T^{\prime}}{T}=\sqrt{\dfrac{g}{g^{\prime}}}=\sqrt{\dfrac{g}{g} \times 4}=2\) \(T^{\prime}=2 T\) So, \(x=2\)
JEE - 2023
PHXI08:GRAVITATION
359625
Assertion : If a pendulum is suspended in a lift and lift falling freely, then its time period becomes infinite. Reason : Free falling body has acceleration equal to acceleration due to gravity.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The pendulum's time period (T) in a descending elevator is calculated by \(T=2 \pi \sqrt{\dfrac{l}{g-a}}\), where 'l' is length, ' \(g\) ' is gravity, and ' \(\mathrm{a}\) ' is elevator acceleration. In free fall \((a=\) \(g\) ), \(\mathrm{T}\) becomes infinite, leading to an indefinitely long pendulum period. So correct option is (1)
PHXI08:GRAVITATION
359626
Assertion : There is no effect (felt) of rotation of earth on acceleration due to gravity at poles. Reason : Rotation of earth is about polar axis.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rotation (with \(\omega\) ) of the Earth about its axis does not affect the acceleration due to gravity at the poles. At poles \(\lambda=90^{\circ}\) \(\Rightarrow \cos \lambda=0\) \(\Rightarrow g^{\prime}=g\) Body at poles does not feel centrifugal force. The direction of rotation is perpendicular to the force of gravity. So correct option is (1).
PHXI08:GRAVITATION
359627
Match the Column I with Column II. Column I Column II A Weight P Minimum B \({{\rm{g}}_{{\rm{equator}}}}\) Q Zero C \({{\text{g}}_{{\text{poles}}}}\) R Vector D \({{\text{g}}_{{\text{center}}}}\) S Maximum
1 A - Q, B - P, C - R, D - S
2 A - Q, B - Q, C - S, D - R
3 A - R, B - P, C - S, D - Q
4 A - S, B - R, C - P, D - Q
Explanation:
Weight is a vector quantity. The effective acceleration due to gravity is maximum at poles since centrifugal force is zero . There similary \(g\) at equal for is minimum as centrifugal force is maximum there. option (3) is correct.
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PHXI08:GRAVITATION
359623
Assertion : Space rockets are usually launched in the equatorial line from west to east. Reason : The acceleration due to gravity is minimum at the equator.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Earth's rotation is taking place from west to east. Earth's eastward rotation imparts a maximum velocity at the equator, aiding rockets launched west to east. This effect eases the launch process due to the added linear velocity from Earth's rotation. Reason is separate fact. So correct option is (2).
PHXI08:GRAVITATION
359624
\(T\) is the time period of simple pendulum on the earth's surface. Its time period becomes \(x T\) when taken to a height \(R\) (equal to earth's radius) above the earth's surface. Then, the value of \(x\) will be
1 \(\dfrac{1}{2}\)
2 4
3 \(\dfrac{1}{4}\)
4 2
Explanation:
Time period on earth's surface \(=T\), Height, \(h=R\) Let the new period is \(T^{\prime}\). At height \(h=R\), value of \(g\) becomes \(g^{\prime}\) \(g^{\prime}=g\left(\dfrac{R}{R+h}\right)^{2}=g\left(\dfrac{R}{R+R}\right)^{2}=\dfrac{g}{4}\) As, time period, \(T \propto \dfrac{1}{\sqrt{g}} \quad\left(\because T=2 \pi \sqrt{\dfrac{l}{g}}\right)\) \(\dfrac{T^{\prime}}{T}=\sqrt{\dfrac{g}{g^{\prime}}}=\sqrt{\dfrac{g}{g} \times 4}=2\) \(T^{\prime}=2 T\) So, \(x=2\)
JEE - 2023
PHXI08:GRAVITATION
359625
Assertion : If a pendulum is suspended in a lift and lift falling freely, then its time period becomes infinite. Reason : Free falling body has acceleration equal to acceleration due to gravity.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The pendulum's time period (T) in a descending elevator is calculated by \(T=2 \pi \sqrt{\dfrac{l}{g-a}}\), where 'l' is length, ' \(g\) ' is gravity, and ' \(\mathrm{a}\) ' is elevator acceleration. In free fall \((a=\) \(g\) ), \(\mathrm{T}\) becomes infinite, leading to an indefinitely long pendulum period. So correct option is (1)
PHXI08:GRAVITATION
359626
Assertion : There is no effect (felt) of rotation of earth on acceleration due to gravity at poles. Reason : Rotation of earth is about polar axis.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rotation (with \(\omega\) ) of the Earth about its axis does not affect the acceleration due to gravity at the poles. At poles \(\lambda=90^{\circ}\) \(\Rightarrow \cos \lambda=0\) \(\Rightarrow g^{\prime}=g\) Body at poles does not feel centrifugal force. The direction of rotation is perpendicular to the force of gravity. So correct option is (1).
PHXI08:GRAVITATION
359627
Match the Column I with Column II. Column I Column II A Weight P Minimum B \({{\rm{g}}_{{\rm{equator}}}}\) Q Zero C \({{\text{g}}_{{\text{poles}}}}\) R Vector D \({{\text{g}}_{{\text{center}}}}\) S Maximum
1 A - Q, B - P, C - R, D - S
2 A - Q, B - Q, C - S, D - R
3 A - R, B - P, C - S, D - Q
4 A - S, B - R, C - P, D - Q
Explanation:
Weight is a vector quantity. The effective acceleration due to gravity is maximum at poles since centrifugal force is zero . There similary \(g\) at equal for is minimum as centrifugal force is maximum there. option (3) is correct.
359623
Assertion : Space rockets are usually launched in the equatorial line from west to east. Reason : The acceleration due to gravity is minimum at the equator.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Earth's rotation is taking place from west to east. Earth's eastward rotation imparts a maximum velocity at the equator, aiding rockets launched west to east. This effect eases the launch process due to the added linear velocity from Earth's rotation. Reason is separate fact. So correct option is (2).
PHXI08:GRAVITATION
359624
\(T\) is the time period of simple pendulum on the earth's surface. Its time period becomes \(x T\) when taken to a height \(R\) (equal to earth's radius) above the earth's surface. Then, the value of \(x\) will be
1 \(\dfrac{1}{2}\)
2 4
3 \(\dfrac{1}{4}\)
4 2
Explanation:
Time period on earth's surface \(=T\), Height, \(h=R\) Let the new period is \(T^{\prime}\). At height \(h=R\), value of \(g\) becomes \(g^{\prime}\) \(g^{\prime}=g\left(\dfrac{R}{R+h}\right)^{2}=g\left(\dfrac{R}{R+R}\right)^{2}=\dfrac{g}{4}\) As, time period, \(T \propto \dfrac{1}{\sqrt{g}} \quad\left(\because T=2 \pi \sqrt{\dfrac{l}{g}}\right)\) \(\dfrac{T^{\prime}}{T}=\sqrt{\dfrac{g}{g^{\prime}}}=\sqrt{\dfrac{g}{g} \times 4}=2\) \(T^{\prime}=2 T\) So, \(x=2\)
JEE - 2023
PHXI08:GRAVITATION
359625
Assertion : If a pendulum is suspended in a lift and lift falling freely, then its time period becomes infinite. Reason : Free falling body has acceleration equal to acceleration due to gravity.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The pendulum's time period (T) in a descending elevator is calculated by \(T=2 \pi \sqrt{\dfrac{l}{g-a}}\), where 'l' is length, ' \(g\) ' is gravity, and ' \(\mathrm{a}\) ' is elevator acceleration. In free fall \((a=\) \(g\) ), \(\mathrm{T}\) becomes infinite, leading to an indefinitely long pendulum period. So correct option is (1)
PHXI08:GRAVITATION
359626
Assertion : There is no effect (felt) of rotation of earth on acceleration due to gravity at poles. Reason : Rotation of earth is about polar axis.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rotation (with \(\omega\) ) of the Earth about its axis does not affect the acceleration due to gravity at the poles. At poles \(\lambda=90^{\circ}\) \(\Rightarrow \cos \lambda=0\) \(\Rightarrow g^{\prime}=g\) Body at poles does not feel centrifugal force. The direction of rotation is perpendicular to the force of gravity. So correct option is (1).
PHXI08:GRAVITATION
359627
Match the Column I with Column II. Column I Column II A Weight P Minimum B \({{\rm{g}}_{{\rm{equator}}}}\) Q Zero C \({{\text{g}}_{{\text{poles}}}}\) R Vector D \({{\text{g}}_{{\text{center}}}}\) S Maximum
1 A - Q, B - P, C - R, D - S
2 A - Q, B - Q, C - S, D - R
3 A - R, B - P, C - S, D - Q
4 A - S, B - R, C - P, D - Q
Explanation:
Weight is a vector quantity. The effective acceleration due to gravity is maximum at poles since centrifugal force is zero . There similary \(g\) at equal for is minimum as centrifugal force is maximum there. option (3) is correct.
359623
Assertion : Space rockets are usually launched in the equatorial line from west to east. Reason : The acceleration due to gravity is minimum at the equator.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Earth's rotation is taking place from west to east. Earth's eastward rotation imparts a maximum velocity at the equator, aiding rockets launched west to east. This effect eases the launch process due to the added linear velocity from Earth's rotation. Reason is separate fact. So correct option is (2).
PHXI08:GRAVITATION
359624
\(T\) is the time period of simple pendulum on the earth's surface. Its time period becomes \(x T\) when taken to a height \(R\) (equal to earth's radius) above the earth's surface. Then, the value of \(x\) will be
1 \(\dfrac{1}{2}\)
2 4
3 \(\dfrac{1}{4}\)
4 2
Explanation:
Time period on earth's surface \(=T\), Height, \(h=R\) Let the new period is \(T^{\prime}\). At height \(h=R\), value of \(g\) becomes \(g^{\prime}\) \(g^{\prime}=g\left(\dfrac{R}{R+h}\right)^{2}=g\left(\dfrac{R}{R+R}\right)^{2}=\dfrac{g}{4}\) As, time period, \(T \propto \dfrac{1}{\sqrt{g}} \quad\left(\because T=2 \pi \sqrt{\dfrac{l}{g}}\right)\) \(\dfrac{T^{\prime}}{T}=\sqrt{\dfrac{g}{g^{\prime}}}=\sqrt{\dfrac{g}{g} \times 4}=2\) \(T^{\prime}=2 T\) So, \(x=2\)
JEE - 2023
PHXI08:GRAVITATION
359625
Assertion : If a pendulum is suspended in a lift and lift falling freely, then its time period becomes infinite. Reason : Free falling body has acceleration equal to acceleration due to gravity.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The pendulum's time period (T) in a descending elevator is calculated by \(T=2 \pi \sqrt{\dfrac{l}{g-a}}\), where 'l' is length, ' \(g\) ' is gravity, and ' \(\mathrm{a}\) ' is elevator acceleration. In free fall \((a=\) \(g\) ), \(\mathrm{T}\) becomes infinite, leading to an indefinitely long pendulum period. So correct option is (1)
PHXI08:GRAVITATION
359626
Assertion : There is no effect (felt) of rotation of earth on acceleration due to gravity at poles. Reason : Rotation of earth is about polar axis.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The rotation (with \(\omega\) ) of the Earth about its axis does not affect the acceleration due to gravity at the poles. At poles \(\lambda=90^{\circ}\) \(\Rightarrow \cos \lambda=0\) \(\Rightarrow g^{\prime}=g\) Body at poles does not feel centrifugal force. The direction of rotation is perpendicular to the force of gravity. So correct option is (1).
PHXI08:GRAVITATION
359627
Match the Column I with Column II. Column I Column II A Weight P Minimum B \({{\rm{g}}_{{\rm{equator}}}}\) Q Zero C \({{\text{g}}_{{\text{poles}}}}\) R Vector D \({{\text{g}}_{{\text{center}}}}\) S Maximum
1 A - Q, B - P, C - R, D - S
2 A - Q, B - Q, C - S, D - R
3 A - R, B - P, C - S, D - Q
4 A - S, B - R, C - P, D - Q
Explanation:
Weight is a vector quantity. The effective acceleration due to gravity is maximum at poles since centrifugal force is zero . There similary \(g\) at equal for is minimum as centrifugal force is maximum there. option (3) is correct.