359991
Assertion : The ratio of inertial mass to gravitational mass is equal to one. Reason : The inertial mass and gravitational mass of a body are conceptually different.
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:
Inertial mass \(\left(m_{0}\right)\) indicates object's resistance to change its velocity. But, gravitational mass \((m)\) is in universal law. \(m_{0}\) is in Newton's law \(F=m_{0} a\) where \(a=\dfrac{d v}{d t}\). But, \(m\) is in formula \(F=m g=\dfrac{G M_{e} m}{R_{E}^{2}}\) (written here on earth of mass \(M_{e}\) ). At a given place, \(\mathrm{m}\) and \(m_{0}\) are taken to be equivalent. So correct option is (2).
PHXI08:GRAVITATION
359992
How will you weigh of sun i.e., estimate its mass? You will need to know the period of one of its planets and the radius of the planetary orbit. The mean orbital radius of the earth around the sun is \(1.5 \times {10^8}\;km\). Then the mass of the sun is
1 \(5 \times {10^{30}}\;kg\)
2 \(4 \times {10^{30}}\;kg\)
3 \(3 \times {10^{30}}\;kg\)
4 \(2 \times {10^{30}}\;kg\)
Explanation:
Mean orbital radius of the earth around the sun \(r = 1.5 \times {10^8}\;km = 1.5 \times {10^{11}}\;m\) Time period of earth around the sun \( = 1yr\) \(=\)365 days \( = 365 \times 24 \times 60 \times 60\;s\) The orbital velocity is \({v^2} = \frac{{G{M_s}}}{r}\) \(\therefore \quad {\left( {\frac{{2\pi }}{T}} \right)^2} = \frac{{G{M_s}}}{{{r^3}}}\quad \left( {v = \frac{{2\pi r}}{T}} \right)\) \( \Rightarrow \quad {M_s} = \frac{{4{\pi ^2}{r^3}}}{{G{T^2}}}\) \( = \frac{{4 \times {{(3.14)}^2} \times {{(1.5 \times {{10}^{11}})}^3}}}{{6.67 \times {{10}^{ - 11}} \times {{(365 \times 24 \times 60 \times 60)}^2}}} = 2 \times {10^{30}}kg\)
NCERT Exemplar
PHXI08:GRAVITATION
359993
Assertion : The length (i.e, duration) of the day is slowly increasing, due to rotational effect. Reason : The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.
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:
\(T=\dfrac{2 \pi}{\omega}, T\) depends on \(\omega\). The length (duration of) the day is indeed increasing, but the primary cause is the transfer of angular momentum between the Earth and the Moon due to tidal forces, not the gravitational pull of other planets. So correct option is (3).
PHXI08:GRAVITATION
359994
Assertion : The earth without its atmosphere would be inhospitably cold. Reason : All heat would escape in the absence of atmosphere.
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 Earth's atmosphere helps to retain heat through the greenhouse effect. Heat radiated out by earth is reflected back by the atmosphere without it, the surface would be much colder as all heat escapes. So correct option is (1).
PHXI08:GRAVITATION
359995
Assertion : The motion of a particle under the central force is always confined to a plane. Reason : Angular momentum is always conserved in the motion under a central force.
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:
\(\vec{\tau}=\dfrac{d \vec{L}}{d t}=[\vec{r} \times \vec{F}(r)]\) In a central force field \(\vec{F}(r)\), the rotational motion (caused by \(\vec{\tau}\) ) of a particle is always confined to a plane due to the conservation of angular momentum as \(F\) is function of \(r\) only. So correct option is (1).
359991
Assertion : The ratio of inertial mass to gravitational mass is equal to one. Reason : The inertial mass and gravitational mass of a body are conceptually different.
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:
Inertial mass \(\left(m_{0}\right)\) indicates object's resistance to change its velocity. But, gravitational mass \((m)\) is in universal law. \(m_{0}\) is in Newton's law \(F=m_{0} a\) where \(a=\dfrac{d v}{d t}\). But, \(m\) is in formula \(F=m g=\dfrac{G M_{e} m}{R_{E}^{2}}\) (written here on earth of mass \(M_{e}\) ). At a given place, \(\mathrm{m}\) and \(m_{0}\) are taken to be equivalent. So correct option is (2).
PHXI08:GRAVITATION
359992
How will you weigh of sun i.e., estimate its mass? You will need to know the period of one of its planets and the radius of the planetary orbit. The mean orbital radius of the earth around the sun is \(1.5 \times {10^8}\;km\). Then the mass of the sun is
1 \(5 \times {10^{30}}\;kg\)
2 \(4 \times {10^{30}}\;kg\)
3 \(3 \times {10^{30}}\;kg\)
4 \(2 \times {10^{30}}\;kg\)
Explanation:
Mean orbital radius of the earth around the sun \(r = 1.5 \times {10^8}\;km = 1.5 \times {10^{11}}\;m\) Time period of earth around the sun \( = 1yr\) \(=\)365 days \( = 365 \times 24 \times 60 \times 60\;s\) The orbital velocity is \({v^2} = \frac{{G{M_s}}}{r}\) \(\therefore \quad {\left( {\frac{{2\pi }}{T}} \right)^2} = \frac{{G{M_s}}}{{{r^3}}}\quad \left( {v = \frac{{2\pi r}}{T}} \right)\) \( \Rightarrow \quad {M_s} = \frac{{4{\pi ^2}{r^3}}}{{G{T^2}}}\) \( = \frac{{4 \times {{(3.14)}^2} \times {{(1.5 \times {{10}^{11}})}^3}}}{{6.67 \times {{10}^{ - 11}} \times {{(365 \times 24 \times 60 \times 60)}^2}}} = 2 \times {10^{30}}kg\)
NCERT Exemplar
PHXI08:GRAVITATION
359993
Assertion : The length (i.e, duration) of the day is slowly increasing, due to rotational effect. Reason : The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.
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:
\(T=\dfrac{2 \pi}{\omega}, T\) depends on \(\omega\). The length (duration of) the day is indeed increasing, but the primary cause is the transfer of angular momentum between the Earth and the Moon due to tidal forces, not the gravitational pull of other planets. So correct option is (3).
PHXI08:GRAVITATION
359994
Assertion : The earth without its atmosphere would be inhospitably cold. Reason : All heat would escape in the absence of atmosphere.
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 Earth's atmosphere helps to retain heat through the greenhouse effect. Heat radiated out by earth is reflected back by the atmosphere without it, the surface would be much colder as all heat escapes. So correct option is (1).
PHXI08:GRAVITATION
359995
Assertion : The motion of a particle under the central force is always confined to a plane. Reason : Angular momentum is always conserved in the motion under a central force.
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:
\(\vec{\tau}=\dfrac{d \vec{L}}{d t}=[\vec{r} \times \vec{F}(r)]\) In a central force field \(\vec{F}(r)\), the rotational motion (caused by \(\vec{\tau}\) ) of a particle is always confined to a plane due to the conservation of angular momentum as \(F\) is function of \(r\) only. So correct option is (1).
359991
Assertion : The ratio of inertial mass to gravitational mass is equal to one. Reason : The inertial mass and gravitational mass of a body are conceptually different.
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:
Inertial mass \(\left(m_{0}\right)\) indicates object's resistance to change its velocity. But, gravitational mass \((m)\) is in universal law. \(m_{0}\) is in Newton's law \(F=m_{0} a\) where \(a=\dfrac{d v}{d t}\). But, \(m\) is in formula \(F=m g=\dfrac{G M_{e} m}{R_{E}^{2}}\) (written here on earth of mass \(M_{e}\) ). At a given place, \(\mathrm{m}\) and \(m_{0}\) are taken to be equivalent. So correct option is (2).
PHXI08:GRAVITATION
359992
How will you weigh of sun i.e., estimate its mass? You will need to know the period of one of its planets and the radius of the planetary orbit. The mean orbital radius of the earth around the sun is \(1.5 \times {10^8}\;km\). Then the mass of the sun is
1 \(5 \times {10^{30}}\;kg\)
2 \(4 \times {10^{30}}\;kg\)
3 \(3 \times {10^{30}}\;kg\)
4 \(2 \times {10^{30}}\;kg\)
Explanation:
Mean orbital radius of the earth around the sun \(r = 1.5 \times {10^8}\;km = 1.5 \times {10^{11}}\;m\) Time period of earth around the sun \( = 1yr\) \(=\)365 days \( = 365 \times 24 \times 60 \times 60\;s\) The orbital velocity is \({v^2} = \frac{{G{M_s}}}{r}\) \(\therefore \quad {\left( {\frac{{2\pi }}{T}} \right)^2} = \frac{{G{M_s}}}{{{r^3}}}\quad \left( {v = \frac{{2\pi r}}{T}} \right)\) \( \Rightarrow \quad {M_s} = \frac{{4{\pi ^2}{r^3}}}{{G{T^2}}}\) \( = \frac{{4 \times {{(3.14)}^2} \times {{(1.5 \times {{10}^{11}})}^3}}}{{6.67 \times {{10}^{ - 11}} \times {{(365 \times 24 \times 60 \times 60)}^2}}} = 2 \times {10^{30}}kg\)
NCERT Exemplar
PHXI08:GRAVITATION
359993
Assertion : The length (i.e, duration) of the day is slowly increasing, due to rotational effect. Reason : The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.
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:
\(T=\dfrac{2 \pi}{\omega}, T\) depends on \(\omega\). The length (duration of) the day is indeed increasing, but the primary cause is the transfer of angular momentum between the Earth and the Moon due to tidal forces, not the gravitational pull of other planets. So correct option is (3).
PHXI08:GRAVITATION
359994
Assertion : The earth without its atmosphere would be inhospitably cold. Reason : All heat would escape in the absence of atmosphere.
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 Earth's atmosphere helps to retain heat through the greenhouse effect. Heat radiated out by earth is reflected back by the atmosphere without it, the surface would be much colder as all heat escapes. So correct option is (1).
PHXI08:GRAVITATION
359995
Assertion : The motion of a particle under the central force is always confined to a plane. Reason : Angular momentum is always conserved in the motion under a central force.
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:
\(\vec{\tau}=\dfrac{d \vec{L}}{d t}=[\vec{r} \times \vec{F}(r)]\) In a central force field \(\vec{F}(r)\), the rotational motion (caused by \(\vec{\tau}\) ) of a particle is always confined to a plane due to the conservation of angular momentum as \(F\) is function of \(r\) only. So correct option is (1).
359991
Assertion : The ratio of inertial mass to gravitational mass is equal to one. Reason : The inertial mass and gravitational mass of a body are conceptually different.
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:
Inertial mass \(\left(m_{0}\right)\) indicates object's resistance to change its velocity. But, gravitational mass \((m)\) is in universal law. \(m_{0}\) is in Newton's law \(F=m_{0} a\) where \(a=\dfrac{d v}{d t}\). But, \(m\) is in formula \(F=m g=\dfrac{G M_{e} m}{R_{E}^{2}}\) (written here on earth of mass \(M_{e}\) ). At a given place, \(\mathrm{m}\) and \(m_{0}\) are taken to be equivalent. So correct option is (2).
PHXI08:GRAVITATION
359992
How will you weigh of sun i.e., estimate its mass? You will need to know the period of one of its planets and the radius of the planetary orbit. The mean orbital radius of the earth around the sun is \(1.5 \times {10^8}\;km\). Then the mass of the sun is
1 \(5 \times {10^{30}}\;kg\)
2 \(4 \times {10^{30}}\;kg\)
3 \(3 \times {10^{30}}\;kg\)
4 \(2 \times {10^{30}}\;kg\)
Explanation:
Mean orbital radius of the earth around the sun \(r = 1.5 \times {10^8}\;km = 1.5 \times {10^{11}}\;m\) Time period of earth around the sun \( = 1yr\) \(=\)365 days \( = 365 \times 24 \times 60 \times 60\;s\) The orbital velocity is \({v^2} = \frac{{G{M_s}}}{r}\) \(\therefore \quad {\left( {\frac{{2\pi }}{T}} \right)^2} = \frac{{G{M_s}}}{{{r^3}}}\quad \left( {v = \frac{{2\pi r}}{T}} \right)\) \( \Rightarrow \quad {M_s} = \frac{{4{\pi ^2}{r^3}}}{{G{T^2}}}\) \( = \frac{{4 \times {{(3.14)}^2} \times {{(1.5 \times {{10}^{11}})}^3}}}{{6.67 \times {{10}^{ - 11}} \times {{(365 \times 24 \times 60 \times 60)}^2}}} = 2 \times {10^{30}}kg\)
NCERT Exemplar
PHXI08:GRAVITATION
359993
Assertion : The length (i.e, duration) of the day is slowly increasing, due to rotational effect. Reason : The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.
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:
\(T=\dfrac{2 \pi}{\omega}, T\) depends on \(\omega\). The length (duration of) the day is indeed increasing, but the primary cause is the transfer of angular momentum between the Earth and the Moon due to tidal forces, not the gravitational pull of other planets. So correct option is (3).
PHXI08:GRAVITATION
359994
Assertion : The earth without its atmosphere would be inhospitably cold. Reason : All heat would escape in the absence of atmosphere.
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 Earth's atmosphere helps to retain heat through the greenhouse effect. Heat radiated out by earth is reflected back by the atmosphere without it, the surface would be much colder as all heat escapes. So correct option is (1).
PHXI08:GRAVITATION
359995
Assertion : The motion of a particle under the central force is always confined to a plane. Reason : Angular momentum is always conserved in the motion under a central force.
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:
\(\vec{\tau}=\dfrac{d \vec{L}}{d t}=[\vec{r} \times \vec{F}(r)]\) In a central force field \(\vec{F}(r)\), the rotational motion (caused by \(\vec{\tau}\) ) of a particle is always confined to a plane due to the conservation of angular momentum as \(F\) is function of \(r\) only. So correct option is (1).
359991
Assertion : The ratio of inertial mass to gravitational mass is equal to one. Reason : The inertial mass and gravitational mass of a body are conceptually different.
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:
Inertial mass \(\left(m_{0}\right)\) indicates object's resistance to change its velocity. But, gravitational mass \((m)\) is in universal law. \(m_{0}\) is in Newton's law \(F=m_{0} a\) where \(a=\dfrac{d v}{d t}\). But, \(m\) is in formula \(F=m g=\dfrac{G M_{e} m}{R_{E}^{2}}\) (written here on earth of mass \(M_{e}\) ). At a given place, \(\mathrm{m}\) and \(m_{0}\) are taken to be equivalent. So correct option is (2).
PHXI08:GRAVITATION
359992
How will you weigh of sun i.e., estimate its mass? You will need to know the period of one of its planets and the radius of the planetary orbit. The mean orbital radius of the earth around the sun is \(1.5 \times {10^8}\;km\). Then the mass of the sun is
1 \(5 \times {10^{30}}\;kg\)
2 \(4 \times {10^{30}}\;kg\)
3 \(3 \times {10^{30}}\;kg\)
4 \(2 \times {10^{30}}\;kg\)
Explanation:
Mean orbital radius of the earth around the sun \(r = 1.5 \times {10^8}\;km = 1.5 \times {10^{11}}\;m\) Time period of earth around the sun \( = 1yr\) \(=\)365 days \( = 365 \times 24 \times 60 \times 60\;s\) The orbital velocity is \({v^2} = \frac{{G{M_s}}}{r}\) \(\therefore \quad {\left( {\frac{{2\pi }}{T}} \right)^2} = \frac{{G{M_s}}}{{{r^3}}}\quad \left( {v = \frac{{2\pi r}}{T}} \right)\) \( \Rightarrow \quad {M_s} = \frac{{4{\pi ^2}{r^3}}}{{G{T^2}}}\) \( = \frac{{4 \times {{(3.14)}^2} \times {{(1.5 \times {{10}^{11}})}^3}}}{{6.67 \times {{10}^{ - 11}} \times {{(365 \times 24 \times 60 \times 60)}^2}}} = 2 \times {10^{30}}kg\)
NCERT Exemplar
PHXI08:GRAVITATION
359993
Assertion : The length (i.e, duration) of the day is slowly increasing, due to rotational effect. Reason : The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.
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:
\(T=\dfrac{2 \pi}{\omega}, T\) depends on \(\omega\). The length (duration of) the day is indeed increasing, but the primary cause is the transfer of angular momentum between the Earth and the Moon due to tidal forces, not the gravitational pull of other planets. So correct option is (3).
PHXI08:GRAVITATION
359994
Assertion : The earth without its atmosphere would be inhospitably cold. Reason : All heat would escape in the absence of atmosphere.
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 Earth's atmosphere helps to retain heat through the greenhouse effect. Heat radiated out by earth is reflected back by the atmosphere without it, the surface would be much colder as all heat escapes. So correct option is (1).
PHXI08:GRAVITATION
359995
Assertion : The motion of a particle under the central force is always confined to a plane. Reason : Angular momentum is always conserved in the motion under a central force.
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:
\(\vec{\tau}=\dfrac{d \vec{L}}{d t}=[\vec{r} \times \vec{F}(r)]\) In a central force field \(\vec{F}(r)\), the rotational motion (caused by \(\vec{\tau}\) ) of a particle is always confined to a plane due to the conservation of angular momentum as \(F\) is function of \(r\) only. So correct option is (1).
