Gravitational Potential
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PHXI08:GRAVITATION

359897 Two hypothetical planets of masses \({m_1}\) and \({m_2}\) are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is ' \(d\) '? (Speed of \(m_{1}\) is \(v_{1}\) and that of \({m_2}\) is \({v_2}\)):-
supporting img

1 \({v_1} = {m_2}\sqrt {\frac{{2G}}{{{m_1}}}} ;{v_2} = {m_1}\sqrt {\frac{{2G}}{{{m_2}}}} \)
2 \(v_{1}=v_{2}\)
3 \(v_{1}=m_{1} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}} ; v_{2}=m_{2} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}}\)
4 \(v_{1}=m_{2} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}} ; v_{2}=m_{1} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}}\)
JEE - 2014
PHXI08:GRAVITATION

359898 Three particles each of mass \(m\) are present a \(t\) the corners of an equilateral triangle of side \(a\). Gravitational potential energy of the system is
supporting img

1 \(\dfrac{3 G m^{2}}{a}\)
2 \(-\dfrac{3 G m^{2}}{2 a}\)
3 \(-\dfrac{3 G m^{2}}{a}\)
4 \(-\dfrac{G m^{2}}{a}\)
PHXI08:GRAVITATION

359899 A particle of mass ' \(m\) ' is projected with a velocity \(u = k{v_e}(k < 1)\) from the surface of the earth. \(\left( {{v_e}} \right. = \) escape velocity) The maximum height above the surface reached by the particle is

1 \(R\left(\dfrac{k}{1+k}\right)\)
2 \(\dfrac{R^{2} k}{1+k}\)
3 \(\dfrac{R k^{2}}{1-k^{2}}\)
4 \(R\left(\dfrac{k}{1-k}\right)^{2}\)
NEET - 2021
PHXI08:GRAVITATION

359900 A mass \(m\) on the surface of the Earth is shifted to a target equal to the radius of the Earth. If \(R\) is the radius and \(M\) is the mass of the Earth, then work done in this process is

1 \(\frac{{mgR}}{2}\)
2 \(mgR\)
3 \(2mgR\)
4 \(\frac{{mgR}}{4}\)
KCET - 2018
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PHXI08:GRAVITATION

359897 Two hypothetical planets of masses \({m_1}\) and \({m_2}\) are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is ' \(d\) '? (Speed of \(m_{1}\) is \(v_{1}\) and that of \({m_2}\) is \({v_2}\)):-
supporting img

1 \({v_1} = {m_2}\sqrt {\frac{{2G}}{{{m_1}}}} ;{v_2} = {m_1}\sqrt {\frac{{2G}}{{{m_2}}}} \)
2 \(v_{1}=v_{2}\)
3 \(v_{1}=m_{1} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}} ; v_{2}=m_{2} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}}\)
4 \(v_{1}=m_{2} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}} ; v_{2}=m_{1} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}}\)
JEE - 2014
PHXI08:GRAVITATION

359898 Three particles each of mass \(m\) are present a \(t\) the corners of an equilateral triangle of side \(a\). Gravitational potential energy of the system is
supporting img

1 \(\dfrac{3 G m^{2}}{a}\)
2 \(-\dfrac{3 G m^{2}}{2 a}\)
3 \(-\dfrac{3 G m^{2}}{a}\)
4 \(-\dfrac{G m^{2}}{a}\)
PHXI08:GRAVITATION

359899 A particle of mass ' \(m\) ' is projected with a velocity \(u = k{v_e}(k < 1)\) from the surface of the earth. \(\left( {{v_e}} \right. = \) escape velocity) The maximum height above the surface reached by the particle is

1 \(R\left(\dfrac{k}{1+k}\right)\)
2 \(\dfrac{R^{2} k}{1+k}\)
3 \(\dfrac{R k^{2}}{1-k^{2}}\)
4 \(R\left(\dfrac{k}{1-k}\right)^{2}\)
NEET - 2021
PHXI08:GRAVITATION

359900 A mass \(m\) on the surface of the Earth is shifted to a target equal to the radius of the Earth. If \(R\) is the radius and \(M\) is the mass of the Earth, then work done in this process is

1 \(\frac{{mgR}}{2}\)
2 \(mgR\)
3 \(2mgR\)
4 \(\frac{{mgR}}{4}\)
KCET - 2018
NEET DIGITAL LIBRARY
PHXI08:GRAVITATION

359897 Two hypothetical planets of masses \({m_1}\) and \({m_2}\) are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is ' \(d\) '? (Speed of \(m_{1}\) is \(v_{1}\) and that of \({m_2}\) is \({v_2}\)):-
supporting img

1 \({v_1} = {m_2}\sqrt {\frac{{2G}}{{{m_1}}}} ;{v_2} = {m_1}\sqrt {\frac{{2G}}{{{m_2}}}} \)
2 \(v_{1}=v_{2}\)
3 \(v_{1}=m_{1} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}} ; v_{2}=m_{2} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}}\)
4 \(v_{1}=m_{2} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}} ; v_{2}=m_{1} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}}\)
JEE - 2014
PHXI08:GRAVITATION

359898 Three particles each of mass \(m\) are present a \(t\) the corners of an equilateral triangle of side \(a\). Gravitational potential energy of the system is
supporting img

1 \(\dfrac{3 G m^{2}}{a}\)
2 \(-\dfrac{3 G m^{2}}{2 a}\)
3 \(-\dfrac{3 G m^{2}}{a}\)
4 \(-\dfrac{G m^{2}}{a}\)
PHXI08:GRAVITATION

359899 A particle of mass ' \(m\) ' is projected with a velocity \(u = k{v_e}(k < 1)\) from the surface of the earth. \(\left( {{v_e}} \right. = \) escape velocity) The maximum height above the surface reached by the particle is

1 \(R\left(\dfrac{k}{1+k}\right)\)
2 \(\dfrac{R^{2} k}{1+k}\)
3 \(\dfrac{R k^{2}}{1-k^{2}}\)
4 \(R\left(\dfrac{k}{1-k}\right)^{2}\)
NEET - 2021
PHXI08:GRAVITATION

359900 A mass \(m\) on the surface of the Earth is shifted to a target equal to the radius of the Earth. If \(R\) is the radius and \(M\) is the mass of the Earth, then work done in this process is

1 \(\frac{{mgR}}{2}\)
2 \(mgR\)
3 \(2mgR\)
4 \(\frac{{mgR}}{4}\)
KCET - 2018
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PHXI08:GRAVITATION

359897 Two hypothetical planets of masses \({m_1}\) and \({m_2}\) are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is ' \(d\) '? (Speed of \(m_{1}\) is \(v_{1}\) and that of \({m_2}\) is \({v_2}\)):-
supporting img

1 \({v_1} = {m_2}\sqrt {\frac{{2G}}{{{m_1}}}} ;{v_2} = {m_1}\sqrt {\frac{{2G}}{{{m_2}}}} \)
2 \(v_{1}=v_{2}\)
3 \(v_{1}=m_{1} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}} ; v_{2}=m_{2} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}}\)
4 \(v_{1}=m_{2} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}} ; v_{2}=m_{1} \sqrt{\dfrac{2 G}{d\left(m_{1}+m_{2}\right)}}\)
JEE - 2014
PHXI08:GRAVITATION

359898 Three particles each of mass \(m\) are present a \(t\) the corners of an equilateral triangle of side \(a\). Gravitational potential energy of the system is
supporting img

1 \(\dfrac{3 G m^{2}}{a}\)
2 \(-\dfrac{3 G m^{2}}{2 a}\)
3 \(-\dfrac{3 G m^{2}}{a}\)
4 \(-\dfrac{G m^{2}}{a}\)
PHXI08:GRAVITATION

359899 A particle of mass ' \(m\) ' is projected with a velocity \(u = k{v_e}(k < 1)\) from the surface of the earth. \(\left( {{v_e}} \right. = \) escape velocity) The maximum height above the surface reached by the particle is

1 \(R\left(\dfrac{k}{1+k}\right)\)
2 \(\dfrac{R^{2} k}{1+k}\)
3 \(\dfrac{R k^{2}}{1-k^{2}}\)
4 \(R\left(\dfrac{k}{1-k}\right)^{2}\)
NEET - 2021
PHXI08:GRAVITATION

359900 A mass \(m\) on the surface of the Earth is shifted to a target equal to the radius of the Earth. If \(R\) is the radius and \(M\) is the mass of the Earth, then work done in this process is

1 \(\frac{{mgR}}{2}\)
2 \(mgR\)
3 \(2mgR\)
4 \(\frac{{mgR}}{4}\)
KCET - 2018
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