Miscellaneous Problems on Gravitation
PHXI08:GRAVITATION

360000 Assertion :
Earth is flat at the poles.
Reason :
This is due to rotation of earth about its 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.
PHXI08:GRAVITATION

360001 A point \(P(\sqrt{3} R, 0,0)\) lies on the axis of a ring of a mass ' \(M\) ' and radius ' \(R\) '. The ring is located in \(y\)-z plane with its centre at origin ' \(O\) '. A small particle of mass ' \(m\) ' starts from ' \(P\) ' and reaches ' \(O\) ' under gravitational attraction only. Its speed ' \(O\) ' will be

1 \(\sqrt{\dfrac{G M}{R}}\)
2 \(\sqrt{\dfrac{G m}{R}}\)
3 \(\sqrt{\dfrac{G M}{\sqrt{2} R}}\)
4 \(\sqrt{\dfrac{G m}{\sqrt{2} R}}\)
PHXI08:GRAVITATION

360002 Different points in earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the \(CM\) (centre of mass) causing translation and a net torque at the \(CM\) causing rotation around an axis through the \(CM\). For the earth-sun system (approximating the earth as a uniform density sphere)

1 The torque is zero
2 The torque causes the earth to spin
3 The rigid body result is not applicable since the earth is not even approximately a rigid body
4 The torque causes the earth to move around the sun
PHXI08:GRAVITATION

360003 At what temperature, hydrogen molecules will escape from the earth's surface? (Take, radius of earth \( = 6.4 \times {10^6}\;m,\) mass of hydrogen molecule \( = 0.34 \times {10^{ - 26}}\;kg,\) Boltzmann constant \( = 1.38 \times {10^{ - 23}}J{K^{ - 1}}\) and acceleration due to gravity \( = 9.8\;m{s^{ - 2}}\) )

1 \(10 K\)
2 \(10^{2} K\)
3 \({10^3}\;K\)
4 \({10^4}\;K\)
PHXI08:GRAVITATION

360000 Assertion :
Earth is flat at the poles.
Reason :
This is due to rotation of earth about its 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.
PHXI08:GRAVITATION

360001 A point \(P(\sqrt{3} R, 0,0)\) lies on the axis of a ring of a mass ' \(M\) ' and radius ' \(R\) '. The ring is located in \(y\)-z plane with its centre at origin ' \(O\) '. A small particle of mass ' \(m\) ' starts from ' \(P\) ' and reaches ' \(O\) ' under gravitational attraction only. Its speed ' \(O\) ' will be

1 \(\sqrt{\dfrac{G M}{R}}\)
2 \(\sqrt{\dfrac{G m}{R}}\)
3 \(\sqrt{\dfrac{G M}{\sqrt{2} R}}\)
4 \(\sqrt{\dfrac{G m}{\sqrt{2} R}}\)
PHXI08:GRAVITATION

360002 Different points in earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the \(CM\) (centre of mass) causing translation and a net torque at the \(CM\) causing rotation around an axis through the \(CM\). For the earth-sun system (approximating the earth as a uniform density sphere)

1 The torque is zero
2 The torque causes the earth to spin
3 The rigid body result is not applicable since the earth is not even approximately a rigid body
4 The torque causes the earth to move around the sun
PHXI08:GRAVITATION

360003 At what temperature, hydrogen molecules will escape from the earth's surface? (Take, radius of earth \( = 6.4 \times {10^6}\;m,\) mass of hydrogen molecule \( = 0.34 \times {10^{ - 26}}\;kg,\) Boltzmann constant \( = 1.38 \times {10^{ - 23}}J{K^{ - 1}}\) and acceleration due to gravity \( = 9.8\;m{s^{ - 2}}\) )

1 \(10 K\)
2 \(10^{2} K\)
3 \({10^3}\;K\)
4 \({10^4}\;K\)
PHXI08:GRAVITATION

360000 Assertion :
Earth is flat at the poles.
Reason :
This is due to rotation of earth about its 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.
PHXI08:GRAVITATION

360001 A point \(P(\sqrt{3} R, 0,0)\) lies on the axis of a ring of a mass ' \(M\) ' and radius ' \(R\) '. The ring is located in \(y\)-z plane with its centre at origin ' \(O\) '. A small particle of mass ' \(m\) ' starts from ' \(P\) ' and reaches ' \(O\) ' under gravitational attraction only. Its speed ' \(O\) ' will be

1 \(\sqrt{\dfrac{G M}{R}}\)
2 \(\sqrt{\dfrac{G m}{R}}\)
3 \(\sqrt{\dfrac{G M}{\sqrt{2} R}}\)
4 \(\sqrt{\dfrac{G m}{\sqrt{2} R}}\)
PHXI08:GRAVITATION

360002 Different points in earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the \(CM\) (centre of mass) causing translation and a net torque at the \(CM\) causing rotation around an axis through the \(CM\). For the earth-sun system (approximating the earth as a uniform density sphere)

1 The torque is zero
2 The torque causes the earth to spin
3 The rigid body result is not applicable since the earth is not even approximately a rigid body
4 The torque causes the earth to move around the sun
PHXI08:GRAVITATION

360003 At what temperature, hydrogen molecules will escape from the earth's surface? (Take, radius of earth \( = 6.4 \times {10^6}\;m,\) mass of hydrogen molecule \( = 0.34 \times {10^{ - 26}}\;kg,\) Boltzmann constant \( = 1.38 \times {10^{ - 23}}J{K^{ - 1}}\) and acceleration due to gravity \( = 9.8\;m{s^{ - 2}}\) )

1 \(10 K\)
2 \(10^{2} K\)
3 \({10^3}\;K\)
4 \({10^4}\;K\)
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PHXI08:GRAVITATION

360000 Assertion :
Earth is flat at the poles.
Reason :
This is due to rotation of earth about its 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.
PHXI08:GRAVITATION

360001 A point \(P(\sqrt{3} R, 0,0)\) lies on the axis of a ring of a mass ' \(M\) ' and radius ' \(R\) '. The ring is located in \(y\)-z plane with its centre at origin ' \(O\) '. A small particle of mass ' \(m\) ' starts from ' \(P\) ' and reaches ' \(O\) ' under gravitational attraction only. Its speed ' \(O\) ' will be

1 \(\sqrt{\dfrac{G M}{R}}\)
2 \(\sqrt{\dfrac{G m}{R}}\)
3 \(\sqrt{\dfrac{G M}{\sqrt{2} R}}\)
4 \(\sqrt{\dfrac{G m}{\sqrt{2} R}}\)
PHXI08:GRAVITATION

360002 Different points in earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the \(CM\) (centre of mass) causing translation and a net torque at the \(CM\) causing rotation around an axis through the \(CM\). For the earth-sun system (approximating the earth as a uniform density sphere)

1 The torque is zero
2 The torque causes the earth to spin
3 The rigid body result is not applicable since the earth is not even approximately a rigid body
4 The torque causes the earth to move around the sun
PHXI08:GRAVITATION

360003 At what temperature, hydrogen molecules will escape from the earth's surface? (Take, radius of earth \( = 6.4 \times {10^6}\;m,\) mass of hydrogen molecule \( = 0.34 \times {10^{ - 26}}\;kg,\) Boltzmann constant \( = 1.38 \times {10^{ - 23}}J{K^{ - 1}}\) and acceleration due to gravity \( = 9.8\;m{s^{ - 2}}\) )

1 \(10 K\)
2 \(10^{2} K\)
3 \({10^3}\;K\)
4 \({10^4}\;K\)