Coulomb's Law
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PHXII01:ELECTRIC CHARGES AND FIELDS

358052 Two small spheres of masses \({M_1}\,{\rm{and}}\,{M_2}\) are suspended by weightless insulating threads of lengths \({L_1}\,{\rm{and}}\,{L_2}\) . The spheres carry charges \({Q_1}\,{\rm{and}}\,{Q_2}\) respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of \({\theta _1}\,{\rm{and}}\,{\theta _2}\) as shown in figure. Which one of the following conditions is essential, if \({\theta _1}\, = \,{\theta _2}?\)
supporting img

1 \({M_1}\, \ne \,{M_2}\,{\rm{but}}\,{Q_1} = {Q_2}\)
2 \({M_1}\, = \,{M_2}\)
3 \({Q_1}\, = \,{Q_2}\)
4 \({L_1}\, = \,{L_2}\)
KCET - 2010
PHXII01:ELECTRIC CHARGES AND FIELDS

358053 Assertion :
A charge is lying at the centre of the line joining two similar charges each which are fixed. The system will be in equilibrium if that charge is one fourth of the similar charges.
Reason :
For charge to be in equilibrium, sum of the forces on charge due to rest of the two charges must be zero.

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.
PHXII01:ELECTRIC CHARGES AND FIELDS

358054 Two small spheres each of mass \(m\) and with a charge \(q\) lie inside a nonconducting smooth hemispherical bowl of radius \(R\). Find \(q\) if the equilibrium separation between the two charges is \(d\).

1 \(\sqrt {\frac{{2mg\pi {\varepsilon _0}{d^3}}}{{\sqrt {{R^2} - \frac{{{d^2}}}{4}} }}} \)
2 \(\sqrt {\frac{{mg\pi {\varepsilon _0}{d^3}}}{{\sqrt {{R^2} - {d^2}} }}} \)
3 \(\sqrt {\frac{{mg{\varepsilon _0}{d^3}}}{{\sqrt {{R^2} + {d^2}} }}} \)
4 \(\sqrt {mg{\varepsilon _0}{d^3}} \)
PHXII01:ELECTRIC CHARGES AND FIELDS

358055 A charge \(q\) is placed at the centre of the line joining two equal charges \(Q\). The system of three charges will be in equilibrium if \(q\) is equal to

1 \( - \frac{Q}{2}\)
2 \( - \frac{Q}{4}\)
3 \( + \frac{Q}{4}\)
4 \(\frac{Q}{2}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358056 Two positively charged spheres of masses, \({m_1}\,{\rm{and}}\,{m_2}\) are suspended from a common point at the ceiling by identical insulating massless strings of length \(l\). Charges on the two spheres are \({q_1}\,{\rm{and}}\,{q_2}\),respectively. At equilibrium both strings make the same angle \(\theta \) with the vertical.Then

1 \({q_1}{m_1} = {q_2}{m_2}\)
2 \({m_1} = {m_2}\)
3 \({m_1} = {m_2}\sin \theta \)
4 \({q_2}{m_1} = {q_1}{m_2}\)
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PHXII01:ELECTRIC CHARGES AND FIELDS

358052 Two small spheres of masses \({M_1}\,{\rm{and}}\,{M_2}\) are suspended by weightless insulating threads of lengths \({L_1}\,{\rm{and}}\,{L_2}\) . The spheres carry charges \({Q_1}\,{\rm{and}}\,{Q_2}\) respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of \({\theta _1}\,{\rm{and}}\,{\theta _2}\) as shown in figure. Which one of the following conditions is essential, if \({\theta _1}\, = \,{\theta _2}?\)
supporting img

1 \({M_1}\, \ne \,{M_2}\,{\rm{but}}\,{Q_1} = {Q_2}\)
2 \({M_1}\, = \,{M_2}\)
3 \({Q_1}\, = \,{Q_2}\)
4 \({L_1}\, = \,{L_2}\)
KCET - 2010
PHXII01:ELECTRIC CHARGES AND FIELDS

358053 Assertion :
A charge is lying at the centre of the line joining two similar charges each which are fixed. The system will be in equilibrium if that charge is one fourth of the similar charges.
Reason :
For charge to be in equilibrium, sum of the forces on charge due to rest of the two charges must be zero.

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.
PHXII01:ELECTRIC CHARGES AND FIELDS

358054 Two small spheres each of mass \(m\) and with a charge \(q\) lie inside a nonconducting smooth hemispherical bowl of radius \(R\). Find \(q\) if the equilibrium separation between the two charges is \(d\).

1 \(\sqrt {\frac{{2mg\pi {\varepsilon _0}{d^3}}}{{\sqrt {{R^2} - \frac{{{d^2}}}{4}} }}} \)
2 \(\sqrt {\frac{{mg\pi {\varepsilon _0}{d^3}}}{{\sqrt {{R^2} - {d^2}} }}} \)
3 \(\sqrt {\frac{{mg{\varepsilon _0}{d^3}}}{{\sqrt {{R^2} + {d^2}} }}} \)
4 \(\sqrt {mg{\varepsilon _0}{d^3}} \)
PHXII01:ELECTRIC CHARGES AND FIELDS

358055 A charge \(q\) is placed at the centre of the line joining two equal charges \(Q\). The system of three charges will be in equilibrium if \(q\) is equal to

1 \( - \frac{Q}{2}\)
2 \( - \frac{Q}{4}\)
3 \( + \frac{Q}{4}\)
4 \(\frac{Q}{2}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358056 Two positively charged spheres of masses, \({m_1}\,{\rm{and}}\,{m_2}\) are suspended from a common point at the ceiling by identical insulating massless strings of length \(l\). Charges on the two spheres are \({q_1}\,{\rm{and}}\,{q_2}\),respectively. At equilibrium both strings make the same angle \(\theta \) with the vertical.Then

1 \({q_1}{m_1} = {q_2}{m_2}\)
2 \({m_1} = {m_2}\)
3 \({m_1} = {m_2}\sin \theta \)
4 \({q_2}{m_1} = {q_1}{m_2}\)
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PHXII01:ELECTRIC CHARGES AND FIELDS

358052 Two small spheres of masses \({M_1}\,{\rm{and}}\,{M_2}\) are suspended by weightless insulating threads of lengths \({L_1}\,{\rm{and}}\,{L_2}\) . The spheres carry charges \({Q_1}\,{\rm{and}}\,{Q_2}\) respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of \({\theta _1}\,{\rm{and}}\,{\theta _2}\) as shown in figure. Which one of the following conditions is essential, if \({\theta _1}\, = \,{\theta _2}?\)
supporting img

1 \({M_1}\, \ne \,{M_2}\,{\rm{but}}\,{Q_1} = {Q_2}\)
2 \({M_1}\, = \,{M_2}\)
3 \({Q_1}\, = \,{Q_2}\)
4 \({L_1}\, = \,{L_2}\)
KCET - 2010
PHXII01:ELECTRIC CHARGES AND FIELDS

358053 Assertion :
A charge is lying at the centre of the line joining two similar charges each which are fixed. The system will be in equilibrium if that charge is one fourth of the similar charges.
Reason :
For charge to be in equilibrium, sum of the forces on charge due to rest of the two charges must be zero.

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.
PHXII01:ELECTRIC CHARGES AND FIELDS

358054 Two small spheres each of mass \(m\) and with a charge \(q\) lie inside a nonconducting smooth hemispherical bowl of radius \(R\). Find \(q\) if the equilibrium separation between the two charges is \(d\).

1 \(\sqrt {\frac{{2mg\pi {\varepsilon _0}{d^3}}}{{\sqrt {{R^2} - \frac{{{d^2}}}{4}} }}} \)
2 \(\sqrt {\frac{{mg\pi {\varepsilon _0}{d^3}}}{{\sqrt {{R^2} - {d^2}} }}} \)
3 \(\sqrt {\frac{{mg{\varepsilon _0}{d^3}}}{{\sqrt {{R^2} + {d^2}} }}} \)
4 \(\sqrt {mg{\varepsilon _0}{d^3}} \)
PHXII01:ELECTRIC CHARGES AND FIELDS

358055 A charge \(q\) is placed at the centre of the line joining two equal charges \(Q\). The system of three charges will be in equilibrium if \(q\) is equal to

1 \( - \frac{Q}{2}\)
2 \( - \frac{Q}{4}\)
3 \( + \frac{Q}{4}\)
4 \(\frac{Q}{2}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358056 Two positively charged spheres of masses, \({m_1}\,{\rm{and}}\,{m_2}\) are suspended from a common point at the ceiling by identical insulating massless strings of length \(l\). Charges on the two spheres are \({q_1}\,{\rm{and}}\,{q_2}\),respectively. At equilibrium both strings make the same angle \(\theta \) with the vertical.Then

1 \({q_1}{m_1} = {q_2}{m_2}\)
2 \({m_1} = {m_2}\)
3 \({m_1} = {m_2}\sin \theta \)
4 \({q_2}{m_1} = {q_1}{m_2}\)
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PHXII01:ELECTRIC CHARGES AND FIELDS

358052 Two small spheres of masses \({M_1}\,{\rm{and}}\,{M_2}\) are suspended by weightless insulating threads of lengths \({L_1}\,{\rm{and}}\,{L_2}\) . The spheres carry charges \({Q_1}\,{\rm{and}}\,{Q_2}\) respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of \({\theta _1}\,{\rm{and}}\,{\theta _2}\) as shown in figure. Which one of the following conditions is essential, if \({\theta _1}\, = \,{\theta _2}?\)
supporting img

1 \({M_1}\, \ne \,{M_2}\,{\rm{but}}\,{Q_1} = {Q_2}\)
2 \({M_1}\, = \,{M_2}\)
3 \({Q_1}\, = \,{Q_2}\)
4 \({L_1}\, = \,{L_2}\)
KCET - 2010
PHXII01:ELECTRIC CHARGES AND FIELDS

358053 Assertion :
A charge is lying at the centre of the line joining two similar charges each which are fixed. The system will be in equilibrium if that charge is one fourth of the similar charges.
Reason :
For charge to be in equilibrium, sum of the forces on charge due to rest of the two charges must be zero.

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.
PHXII01:ELECTRIC CHARGES AND FIELDS

358054 Two small spheres each of mass \(m\) and with a charge \(q\) lie inside a nonconducting smooth hemispherical bowl of radius \(R\). Find \(q\) if the equilibrium separation between the two charges is \(d\).

1 \(\sqrt {\frac{{2mg\pi {\varepsilon _0}{d^3}}}{{\sqrt {{R^2} - \frac{{{d^2}}}{4}} }}} \)
2 \(\sqrt {\frac{{mg\pi {\varepsilon _0}{d^3}}}{{\sqrt {{R^2} - {d^2}} }}} \)
3 \(\sqrt {\frac{{mg{\varepsilon _0}{d^3}}}{{\sqrt {{R^2} + {d^2}} }}} \)
4 \(\sqrt {mg{\varepsilon _0}{d^3}} \)
PHXII01:ELECTRIC CHARGES AND FIELDS

358055 A charge \(q\) is placed at the centre of the line joining two equal charges \(Q\). The system of three charges will be in equilibrium if \(q\) is equal to

1 \( - \frac{Q}{2}\)
2 \( - \frac{Q}{4}\)
3 \( + \frac{Q}{4}\)
4 \(\frac{Q}{2}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358056 Two positively charged spheres of masses, \({m_1}\,{\rm{and}}\,{m_2}\) are suspended from a common point at the ceiling by identical insulating massless strings of length \(l\). Charges on the two spheres are \({q_1}\,{\rm{and}}\,{q_2}\),respectively. At equilibrium both strings make the same angle \(\theta \) with the vertical.Then

1 \({q_1}{m_1} = {q_2}{m_2}\)
2 \({m_1} = {m_2}\)
3 \({m_1} = {m_2}\sin \theta \)
4 \({q_2}{m_1} = {q_1}{m_2}\)
NEET DIGITAL LIBRARY
PHXII01:ELECTRIC CHARGES AND FIELDS

358052 Two small spheres of masses \({M_1}\,{\rm{and}}\,{M_2}\) are suspended by weightless insulating threads of lengths \({L_1}\,{\rm{and}}\,{L_2}\) . The spheres carry charges \({Q_1}\,{\rm{and}}\,{Q_2}\) respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of \({\theta _1}\,{\rm{and}}\,{\theta _2}\) as shown in figure. Which one of the following conditions is essential, if \({\theta _1}\, = \,{\theta _2}?\)
supporting img

1 \({M_1}\, \ne \,{M_2}\,{\rm{but}}\,{Q_1} = {Q_2}\)
2 \({M_1}\, = \,{M_2}\)
3 \({Q_1}\, = \,{Q_2}\)
4 \({L_1}\, = \,{L_2}\)
KCET - 2010
PHXII01:ELECTRIC CHARGES AND FIELDS

358053 Assertion :
A charge is lying at the centre of the line joining two similar charges each which are fixed. The system will be in equilibrium if that charge is one fourth of the similar charges.
Reason :
For charge to be in equilibrium, sum of the forces on charge due to rest of the two charges must be zero.

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.
PHXII01:ELECTRIC CHARGES AND FIELDS

358054 Two small spheres each of mass \(m\) and with a charge \(q\) lie inside a nonconducting smooth hemispherical bowl of radius \(R\). Find \(q\) if the equilibrium separation between the two charges is \(d\).

1 \(\sqrt {\frac{{2mg\pi {\varepsilon _0}{d^3}}}{{\sqrt {{R^2} - \frac{{{d^2}}}{4}} }}} \)
2 \(\sqrt {\frac{{mg\pi {\varepsilon _0}{d^3}}}{{\sqrt {{R^2} - {d^2}} }}} \)
3 \(\sqrt {\frac{{mg{\varepsilon _0}{d^3}}}{{\sqrt {{R^2} + {d^2}} }}} \)
4 \(\sqrt {mg{\varepsilon _0}{d^3}} \)
PHXII01:ELECTRIC CHARGES AND FIELDS

358055 A charge \(q\) is placed at the centre of the line joining two equal charges \(Q\). The system of three charges will be in equilibrium if \(q\) is equal to

1 \( - \frac{Q}{2}\)
2 \( - \frac{Q}{4}\)
3 \( + \frac{Q}{4}\)
4 \(\frac{Q}{2}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358056 Two positively charged spheres of masses, \({m_1}\,{\rm{and}}\,{m_2}\) are suspended from a common point at the ceiling by identical insulating massless strings of length \(l\). Charges on the two spheres are \({q_1}\,{\rm{and}}\,{q_2}\),respectively. At equilibrium both strings make the same angle \(\theta \) with the vertical.Then

1 \({q_1}{m_1} = {q_2}{m_2}\)
2 \({m_1} = {m_2}\)
3 \({m_1} = {m_2}\sin \theta \)
4 \({q_2}{m_1} = {q_1}{m_2}\)