ELECTROSTATIC FORCE
Electric Charges and Fields

267933 A ball of mass\(m=0.5 \mathrm{~kg}\) is suspended by a thread and a charge \(q=0.1 \mu C\) is supplied. When a ball with diameter \(5 \mathrm{~cm}\) and a like charge of same magnitude is brought close to the first ball, but below it, the tension decreases to \(1 / 3\) of its initial value. Thedistance between centres of the balls is

1 \(0.12 \times 10^{-2} \mathrm{~m}\)
2 \(0.51 \times 10^{-4} \mathrm{~m}\)
3 \(0.2 \times 10^{-5} \mathrm{~m}\)
4 \(0.52 \times 10^{-2} \mathrm{~m}\)
Electric Charges and Fields

267934 Five point charges each \(+q\), are placed on five vertices of a regular hexagon of side \(L\), The magnitude of the force on a point charge of value - q placed at thecentre of the hexagon (in newton) is

1 Zero
2 \(\frac{\sqrt{3} q^{2}}{4 \pi \in_{0} L^{2}}\)
3 \(\frac{q^{2}}{4 \pi \in 0 L^{2}}\)
4 \(\frac{q^{2}}{4 \sqrt{3} \pi \in_{0} L^{2}}\)
Electric Charges and Fields

267935 Two small objects\(X\) and \(Y\) are permanently separated by a distance \(1 \mathrm{~cm}\). 0 bject \(X\) has a charge of \(+1.0 \mu C\) and object \(Y\) hasa charge of \(-1.0 \mu \mathrm{C}\). A certain number of electrons are removed from \(X\) and put onto \(Y\) to make the electrostatic forcebetween the two objects an attractive force whose magnitude is \(360 \mathrm{~N}\). Number of electrons removed is

1 \(8.4 \times 10^{13}\)
2 \(6.25 \times 10^{12}\)
3 \(4.2 \times 10^{11}\)
4 \(3.5 \times 10^{10}\)
Electric Charges and Fields

267936 Two identical positive charges are fixed on the \(\mathrm{y}\)-axis, at equal distance from the origin \(0, \mathrm{~A}\) partical with a negative charge starts on the negative \(x\)-axis at a large distance from 0 , moves along the \(x\)-axis passed through 0 and moves far away from 0 . Its acceleration a is taken as positive along its direction of motion. The particle's acceleration a is plotted against its \(x\)-co-ordinate. W hich of the following best represents the plot?

1
2
3
4
Electric Charges and Fields

267937 Two equal negative charges -\(q\) each are fixed at points \((0,-a)\) and \((0, a)\) on \(y\)-axis. A positive charge \(Q\) is released from rest at the point (2a, 0 ) on the \(x\)-axis. The charge \(Q\) will

1 executesimpleharmonic motionaboutheorigin
2 moveto theoriginand remainat rest
3 moveto infinity
4 execute oscillatory but not simple harmonic motion
Electric Charges and Fields

267933 A ball of mass\(m=0.5 \mathrm{~kg}\) is suspended by a thread and a charge \(q=0.1 \mu C\) is supplied. When a ball with diameter \(5 \mathrm{~cm}\) and a like charge of same magnitude is brought close to the first ball, but below it, the tension decreases to \(1 / 3\) of its initial value. Thedistance between centres of the balls is

1 \(0.12 \times 10^{-2} \mathrm{~m}\)
2 \(0.51 \times 10^{-4} \mathrm{~m}\)
3 \(0.2 \times 10^{-5} \mathrm{~m}\)
4 \(0.52 \times 10^{-2} \mathrm{~m}\)
Electric Charges and Fields

267934 Five point charges each \(+q\), are placed on five vertices of a regular hexagon of side \(L\), The magnitude of the force on a point charge of value - q placed at thecentre of the hexagon (in newton) is

1 Zero
2 \(\frac{\sqrt{3} q^{2}}{4 \pi \in_{0} L^{2}}\)
3 \(\frac{q^{2}}{4 \pi \in 0 L^{2}}\)
4 \(\frac{q^{2}}{4 \sqrt{3} \pi \in_{0} L^{2}}\)
Electric Charges and Fields

267935 Two small objects\(X\) and \(Y\) are permanently separated by a distance \(1 \mathrm{~cm}\). 0 bject \(X\) has a charge of \(+1.0 \mu C\) and object \(Y\) hasa charge of \(-1.0 \mu \mathrm{C}\). A certain number of electrons are removed from \(X\) and put onto \(Y\) to make the electrostatic forcebetween the two objects an attractive force whose magnitude is \(360 \mathrm{~N}\). Number of electrons removed is

1 \(8.4 \times 10^{13}\)
2 \(6.25 \times 10^{12}\)
3 \(4.2 \times 10^{11}\)
4 \(3.5 \times 10^{10}\)
Electric Charges and Fields

267936 Two identical positive charges are fixed on the \(\mathrm{y}\)-axis, at equal distance from the origin \(0, \mathrm{~A}\) partical with a negative charge starts on the negative \(x\)-axis at a large distance from 0 , moves along the \(x\)-axis passed through 0 and moves far away from 0 . Its acceleration a is taken as positive along its direction of motion. The particle's acceleration a is plotted against its \(x\)-co-ordinate. W hich of the following best represents the plot?

1
2
3
4
Electric Charges and Fields

267937 Two equal negative charges -\(q\) each are fixed at points \((0,-a)\) and \((0, a)\) on \(y\)-axis. A positive charge \(Q\) is released from rest at the point (2a, 0 ) on the \(x\)-axis. The charge \(Q\) will

1 executesimpleharmonic motionaboutheorigin
2 moveto theoriginand remainat rest
3 moveto infinity
4 execute oscillatory but not simple harmonic motion
Electric Charges and Fields

267933 A ball of mass\(m=0.5 \mathrm{~kg}\) is suspended by a thread and a charge \(q=0.1 \mu C\) is supplied. When a ball with diameter \(5 \mathrm{~cm}\) and a like charge of same magnitude is brought close to the first ball, but below it, the tension decreases to \(1 / 3\) of its initial value. Thedistance between centres of the balls is

1 \(0.12 \times 10^{-2} \mathrm{~m}\)
2 \(0.51 \times 10^{-4} \mathrm{~m}\)
3 \(0.2 \times 10^{-5} \mathrm{~m}\)
4 \(0.52 \times 10^{-2} \mathrm{~m}\)
Electric Charges and Fields

267934 Five point charges each \(+q\), are placed on five vertices of a regular hexagon of side \(L\), The magnitude of the force on a point charge of value - q placed at thecentre of the hexagon (in newton) is

1 Zero
2 \(\frac{\sqrt{3} q^{2}}{4 \pi \in_{0} L^{2}}\)
3 \(\frac{q^{2}}{4 \pi \in 0 L^{2}}\)
4 \(\frac{q^{2}}{4 \sqrt{3} \pi \in_{0} L^{2}}\)
Electric Charges and Fields

267935 Two small objects\(X\) and \(Y\) are permanently separated by a distance \(1 \mathrm{~cm}\). 0 bject \(X\) has a charge of \(+1.0 \mu C\) and object \(Y\) hasa charge of \(-1.0 \mu \mathrm{C}\). A certain number of electrons are removed from \(X\) and put onto \(Y\) to make the electrostatic forcebetween the two objects an attractive force whose magnitude is \(360 \mathrm{~N}\). Number of electrons removed is

1 \(8.4 \times 10^{13}\)
2 \(6.25 \times 10^{12}\)
3 \(4.2 \times 10^{11}\)
4 \(3.5 \times 10^{10}\)
Electric Charges and Fields

267936 Two identical positive charges are fixed on the \(\mathrm{y}\)-axis, at equal distance from the origin \(0, \mathrm{~A}\) partical with a negative charge starts on the negative \(x\)-axis at a large distance from 0 , moves along the \(x\)-axis passed through 0 and moves far away from 0 . Its acceleration a is taken as positive along its direction of motion. The particle's acceleration a is plotted against its \(x\)-co-ordinate. W hich of the following best represents the plot?

1
2
3
4
Electric Charges and Fields

267937 Two equal negative charges -\(q\) each are fixed at points \((0,-a)\) and \((0, a)\) on \(y\)-axis. A positive charge \(Q\) is released from rest at the point (2a, 0 ) on the \(x\)-axis. The charge \(Q\) will

1 executesimpleharmonic motionaboutheorigin
2 moveto theoriginand remainat rest
3 moveto infinity
4 execute oscillatory but not simple harmonic motion
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Electric Charges and Fields

267933 A ball of mass\(m=0.5 \mathrm{~kg}\) is suspended by a thread and a charge \(q=0.1 \mu C\) is supplied. When a ball with diameter \(5 \mathrm{~cm}\) and a like charge of same magnitude is brought close to the first ball, but below it, the tension decreases to \(1 / 3\) of its initial value. Thedistance between centres of the balls is

1 \(0.12 \times 10^{-2} \mathrm{~m}\)
2 \(0.51 \times 10^{-4} \mathrm{~m}\)
3 \(0.2 \times 10^{-5} \mathrm{~m}\)
4 \(0.52 \times 10^{-2} \mathrm{~m}\)
Electric Charges and Fields

267934 Five point charges each \(+q\), are placed on five vertices of a regular hexagon of side \(L\), The magnitude of the force on a point charge of value - q placed at thecentre of the hexagon (in newton) is

1 Zero
2 \(\frac{\sqrt{3} q^{2}}{4 \pi \in_{0} L^{2}}\)
3 \(\frac{q^{2}}{4 \pi \in 0 L^{2}}\)
4 \(\frac{q^{2}}{4 \sqrt{3} \pi \in_{0} L^{2}}\)
Electric Charges and Fields

267935 Two small objects\(X\) and \(Y\) are permanently separated by a distance \(1 \mathrm{~cm}\). 0 bject \(X\) has a charge of \(+1.0 \mu C\) and object \(Y\) hasa charge of \(-1.0 \mu \mathrm{C}\). A certain number of electrons are removed from \(X\) and put onto \(Y\) to make the electrostatic forcebetween the two objects an attractive force whose magnitude is \(360 \mathrm{~N}\). Number of electrons removed is

1 \(8.4 \times 10^{13}\)
2 \(6.25 \times 10^{12}\)
3 \(4.2 \times 10^{11}\)
4 \(3.5 \times 10^{10}\)
Electric Charges and Fields

267936 Two identical positive charges are fixed on the \(\mathrm{y}\)-axis, at equal distance from the origin \(0, \mathrm{~A}\) partical with a negative charge starts on the negative \(x\)-axis at a large distance from 0 , moves along the \(x\)-axis passed through 0 and moves far away from 0 . Its acceleration a is taken as positive along its direction of motion. The particle's acceleration a is plotted against its \(x\)-co-ordinate. W hich of the following best represents the plot?

1
2
3
4
Electric Charges and Fields

267937 Two equal negative charges -\(q\) each are fixed at points \((0,-a)\) and \((0, a)\) on \(y\)-axis. A positive charge \(Q\) is released from rest at the point (2a, 0 ) on the \(x\)-axis. The charge \(Q\) will

1 executesimpleharmonic motionaboutheorigin
2 moveto theoriginand remainat rest
3 moveto infinity
4 execute oscillatory but not simple harmonic motion
Electric Charges and Fields

267933 A ball of mass\(m=0.5 \mathrm{~kg}\) is suspended by a thread and a charge \(q=0.1 \mu C\) is supplied. When a ball with diameter \(5 \mathrm{~cm}\) and a like charge of same magnitude is brought close to the first ball, but below it, the tension decreases to \(1 / 3\) of its initial value. Thedistance between centres of the balls is

1 \(0.12 \times 10^{-2} \mathrm{~m}\)
2 \(0.51 \times 10^{-4} \mathrm{~m}\)
3 \(0.2 \times 10^{-5} \mathrm{~m}\)
4 \(0.52 \times 10^{-2} \mathrm{~m}\)
Electric Charges and Fields

267934 Five point charges each \(+q\), are placed on five vertices of a regular hexagon of side \(L\), The magnitude of the force on a point charge of value - q placed at thecentre of the hexagon (in newton) is

1 Zero
2 \(\frac{\sqrt{3} q^{2}}{4 \pi \in_{0} L^{2}}\)
3 \(\frac{q^{2}}{4 \pi \in 0 L^{2}}\)
4 \(\frac{q^{2}}{4 \sqrt{3} \pi \in_{0} L^{2}}\)
Electric Charges and Fields

267935 Two small objects\(X\) and \(Y\) are permanently separated by a distance \(1 \mathrm{~cm}\). 0 bject \(X\) has a charge of \(+1.0 \mu C\) and object \(Y\) hasa charge of \(-1.0 \mu \mathrm{C}\). A certain number of electrons are removed from \(X\) and put onto \(Y\) to make the electrostatic forcebetween the two objects an attractive force whose magnitude is \(360 \mathrm{~N}\). Number of electrons removed is

1 \(8.4 \times 10^{13}\)
2 \(6.25 \times 10^{12}\)
3 \(4.2 \times 10^{11}\)
4 \(3.5 \times 10^{10}\)
Electric Charges and Fields

267936 Two identical positive charges are fixed on the \(\mathrm{y}\)-axis, at equal distance from the origin \(0, \mathrm{~A}\) partical with a negative charge starts on the negative \(x\)-axis at a large distance from 0 , moves along the \(x\)-axis passed through 0 and moves far away from 0 . Its acceleration a is taken as positive along its direction of motion. The particle's acceleration a is plotted against its \(x\)-co-ordinate. W hich of the following best represents the plot?

1
2
3
4
Electric Charges and Fields

267937 Two equal negative charges -\(q\) each are fixed at points \((0,-a)\) and \((0, a)\) on \(y\)-axis. A positive charge \(Q\) is released from rest at the point (2a, 0 ) on the \(x\)-axis. The charge \(Q\) will

1 executesimpleharmonic motionaboutheorigin
2 moveto theoriginand remainat rest
3 moveto infinity
4 execute oscillatory but not simple harmonic motion