MHT-CET PYQ’s 2024 Physics - Electrostatics

Electrostatics

1. Two equal point charges ‘\(q\)’ each exert a force ‘\(F\)’ on each other, when they are placed distance ‘\(x\)’ apart in air. When the same charges are placed distance ‘\(y\)’ apart in a medium of dielectric constant ‘\(k\)’, they exert the same force. The ratio of distance ‘\(y\)’ to ‘\(x\)’ is equal to

[MHT-CET 2024, May 3, Shift 1]

  • (1) \( \frac{1}{\sqrt{k}} \)
  • (2) \( \sqrt{k} \)
  • (3) \( \frac{\sqrt{k}}{2} \)
  • (4) \( \frac{2}{\sqrt{k}} \)


2. Two point charges \(+q_1\) and \(q_2\) repel each other with a force of \( 100 \) \(N\). \(q_1\) in increased by \( 10 \)% and \(q_2\) is decreased by \( 10 \)%. If they are kept at their original positions the change in the force of repulsion between them is

[MHT-CET 2024, May 15, Shift 2]

  • (1) decreased by \( 10 \) \( N \)
  • (2) increased by \( 10 \) \( N \)
  • (3) increased by \( 1 \) \( N \)
  • (4) decreasedby \( 1 \) \( N \)


3. Two points charges (\(A\) and \(B\)) \(+4q\) and \(–4q\) are placed along a line separated by a distance ‘\(r\)’. Force acting between them is \(F\). If \( 25 \)% of charge from point \(A\) is transferred to that at point \(B\), the force between the charges now becomes

[MHT-CET 2024, May 10, Shift 2]

  • (1) \( \frac{3}{4} \)\(F\)
  • (2) \( \frac{4}{3} \)\(F\)
  • (3) \( \frac{9}{16} \)\(F\)
  • (4) \( \frac{16}{9} \)\(F\)


4. Charges \( 3 \)\(Q\), \(q\) and \(Q\) are placed along \(x\)-axis at positions \(x\) = \( 0 \), \(x\) = \( \frac{1}{3} \) and \(x\) = \( 1 \) respectively. When the force on charge \(Q\) is zero, the value of \(q\) is 

[MHT-CET 2024, May 11, Shift 1]

  • (1) \( \frac{Q}{3} \)
  • (2) \( - \frac{Q}{3} \)
  • (3) \( \frac{4}{3} \) \(Q\)
  • (4) \( - \frac{4}{3} \) \(Q\)


5. A charge \(+Q\) is placed at each of the diagonally opposite corners of a square. A charge \(-q\) is placed at each of the other diagonally opposite corners as shown. If the net electrical force on \(+Q\) is zero, then \( \frac{+Q}{-q} \) is equal to 

[MHT-CET 2024, May 3, Shift 2]

  • (1) \(+1\)
  • (2) \(+2 \sqrt{2} \)
  • (3) \( \frac{+1}{\sqrt{2}} \)
  • (4) \( -2 \sqrt{2} \)


6. Two charged particles each having charge ‘\(q\)’ and mass ‘\(m\)’ are held at rest while their separation is ‘\(r\)’. The speed of the particles when their separation is \( \frac{'r'}{2} \) will be (\( \epsilon \) = permittivity of the medium) 

[MHT-CET 2024, May 3, Shift 2]

  • (1) \( \frac{q}{4 \pi \epsilon mr} \)
  • (2) \( \frac{q}{2 \pi \epsilon mr} \)
  • (3) \( \frac{q}{ \sqrt{4 \pi \epsilon mr}} \)
  • (4) \( \frac{q^2}{4 \pi \epsilon mr} \)


7. Which of the following statement is correct?

[MHT-CET 2024, May 2, Shift 2]

  • (1) Electric lines of force originate from a – vely charged object and terminate on a + vely charged object
  • (2) The electric line of force do not pass through an insulator but can pass through a conductor
  • (3) The electric line of force do not intersect each other
  • (4) Electric intensity is small in a region where the lines of force are crowded


8. A sphere ‘\(A\)’ of radius ‘\(R\)’ has a charge ‘\(Q\)’ on it. The field at point \(B\) outside the sphere is ‘\(E\)’. Now another sphere of radius ‘\(2R\)’ having a charge ‘\(-2Q\)’ is placed at B. The total field at the point midway between \(A\) and \(B\) due to both the spheres is

[MHT-CET 2024, May 11, Shift 2]

  • (1) \(E\)
  • (2) \( 3 \) \(E\)
  • (3) \( 12 \) \(E\)
  • (4) \( 15 \) \(E\)


9. Two point charges \(+10q\) and \(-4q\) are located at \(x\)=0 and \(x\)=\(L\) respectively. What is the location of a point on the \(x\)-axis from the origin, at which the net electric field due to these two point charges is zero ? (\(r\) = required distance)

[MHT-CET2024,May10,Shift1]

  • (1) \(r\) = \( \frac{\sqrt{2}}{\sqrt{5}-\sqrt{2}} \) right to the point \(B\)
  • (2) \(r\) = \( \frac{\sqrt{2}}{\sqrt{5}-\sqrt{2}} \) right to the point \(A\)
  • (3) \(r\) = \( \frac{\sqrt{2}}{\sqrt{5}+\sqrt{2}} \) right to the point \(B\)
  • (4) \(r\) = \( \frac{\sqrt{2}}{\sqrt{5}+\sqrt{2}} \) right to the point \(A\)


10. Two point charges \(+8q\) and \(-2q\) are located at \(x\)=\( 0 \) and \(x\)=\(L\) respectively. The location of a point on the \(x\)-axis from the origin, at which the net electric field due to these two point charges is zero is

[MHT-CET 2024, May 16, Shift 1]

  • (1) \( \frac{L}{4} \)
  • (2) \( 4 \) \(L\)
  • (3) \( 8 \) \(L\)
  • (4) \( 2 \) \(L\)


11. The point charges \(+q\), \(-q\), \(-q\), \(+q\), \(+Q\) and \(-q\) are placed at the vertices of a regular hexagon \(ABCDEF\) as shown in figure. The electric field at the centre of hexagon ‘\(O\)’ due to the five charges at \(A\), \(B\), \(C\), \(D\) and \(F\) is thrice the electric field at centre ‘\(O\)’ due to charge \(+Q\) at \(E\) alone. The value of \(Q\) is 

[MHT-CET 2024, May 11, Shift 2]

  • (1) \( \frac{+q}{3} \)
  • (2) \( \frac{+q}{5} \)
  • (3) \( \frac{+q}{6} \)
  • (4) \(+6q\)


12. A metallic sphere ‘\(A\)’ isolated from ground, is charged to \( +50μC \). This sphere is brought in contact with other isolated metallic sphere ‘\(B\)’ of half the radius of sphere ‘\(A\)’. Then the charge on the two isolated spheres \(A\) & \(B\) are in the ratio

[MHT-CET 2024, May 4, Shift 1]

  • (1) \( {1 : 2} \)
  • (2) \( {2 : 1} \)
  • (3) \( {4 : 1} \)
  • (4) \( {1 : 1} \)


13. Charges of \( 2μC \) and \( –3μC \) are placed at two points \(A\) and \(B\) separated by \( 1m \). The distance of the point from \(A\), where net potential is zero, is

[MHT-CET 2024, May 15, Shift 2]

  • (1) \(0.7\) \(m\)
  • (2) \(0.5\) \(m\)
  • (3) \(0.4\) \(m\)
  • (4) \(0.6\) \(m\)


14. Three charges \(2q\), \(-q\) and \(-q\) are located at the vertices of an equilateral triangle. At the centre of the triangle

[MHT-CET 2024, May 3, Shift 1]

  • (1) The field is zero but potential is non-zero
  • (2) The field is non-zero but potential is zero
  • (3) Both field and potential are zero
  • (4) Both field and potential are non-zero


15. Four electric charges \(+q\), \(+q\), \(-q\) and \(-q\) are placed in order at the corners of a square of side \(2L\). The electric potential at point midway between the two positive charges is

[MHT-CET 2024, May 10, Shift 1]

  • (1) \( \frac{1}{4πE_0} \) \( \frac{2q}{L} \) (\( 1 + \frac{1}{\sqrt{5}} \))
  • (2) \( \frac{1}{4πE_0} \) \( \frac{2q}{L} \) (\( 1 - \frac{1}{\sqrt{5}} \))
  • (3) \( \frac{1}{4πE_0} \) \( \frac{2q}{L} \) (\( 1 - {\sqrt{5}} \))
  • (4) \( \frac{1}{4πE_0} \) \( \frac{2q}{L} \) (\( 1 + {\sqrt{5}} \))


16. A regular hexagon of side \(10\) \(cm\) has a charge \(1\) \(μC\) at each of its vertices. The potential at the centre of hexagon is [\( \frac{1}{4 \pi \epsilon_0} \) \(9\) x \(10^9\) SI unit]

[MHT-CET 2024, May 3, Shift 2]

  • (1) \(1.8\) x \(10^5\) volt 
  • (2) \(3.6\) x \(10^5\) volt 
  • (3) \(5.4\) x \(10^5\) volt 
  • (4) \(7.2\) x \(10^5\) volt 


17.  ‘\(n\)’ small drops of same size are charged to ‘\(V\)’ volt each. If they coalesce to form a single large drop, then its potential will be

[MHT-CET 2024, May 16, Shift 2]

  • (1) \( V n^1/3\)
  • (2) \( V n^2/3\)
  • (3) \( V n\)
  • (4) \( V n^{-1}\)


18. The electrostatic potential inside a charged spherical ball is given by \(V = ar^2 + b\) where ‘\(r\)’ is the distance from its centre and ‘\(a\) and \(b\)’ are constants. The volume charge density of the ball is [ \( \epsilon_0\) = permittivity of free space ]

[MHT-CET 2024, May 2, Shift 1]

  • (1) \(–24 \pi a\) \(\epsilon_0 r\)
  • (2) \(–6a\) \(\epsilon_0 r\)
  • (3) \(–24 \pi a\) \(\epsilon_0\)
  • (4) \(–6a\) \(\epsilon_0\)


19.  The electric potential at the centre of two concentric half rings of radii \( R_1\) and \(R2\), having same linear charge density ‘\( \lambda \)’ is ( \(\epsilon_0 \) = permittivity of free space ) 

[MHT-CET 2024, May 4, Shift 1]

  • (1) \( \frac{2\lambda}{\epsilon_0}\)
  • (2) \( \frac{\lambda}{2\epsilon_0}\)
  • (3) \( \frac{\lambda}{4\epsilon_0}\)
  • (4) \( \frac{\lambda}{\epsilon_0}\)


20. \(90J\) of work is done to move an electric charge of magnitude \(3C\) from a place \(A\), where potential is – \(10V\) to another place \(B\), where potential is ‘\(V_1\)’ volt. The value of \(V_1\) is

[MHT-CET 2024, May 2, Shift 1]

  • (1) \(10\) \(V\)
  • (2) \(20\) \(V\)
  • (3) \(30\) \(V\)
  • (4) \(-40\) \(V\)


21. The amount of work done in increasing the voltage across the plates of a capacitor form \(5\) \(V\) to \(10\) \(V\) is ‘\(W\)’. The work done in increasing it from \(10\) \(V\) to \(15\) \(V\) will be (nearly)

[MHT-CET 2024, May 2, Shift 2]

  • (1) \(0.6\) \(W\)
  • (2) \(W\)
  • (3) \(1.25\) \(W\)
  • (4) \(1.67\) \(W\)


22. In an electric field due to charge \(Q\), \(a\) charge \(q\) moves from point \(A\) to \(B\) as shown in the figure. The work done is (\( \epsilon_0 \) = permittivity of free space)

[MHT-CET 2024, May 15, Shift 2]

  • (1) \( \frac{1}{4\pi \epsilon_0} \) \( \frac{Qq}{r^2} \)
  • (2) \( \frac{1}{4\pi \epsilon_0} \) \( \frac{Qq}{r^2} \) \( \frac{\pi}{6} \)
  • (3) \( \frac{1}{4\pi \epsilon_0} \) \( \frac{Qq}{r} \)
  • (4) zero


23.  If a \( 10 \) \(μC\) charge exists at the centre of a square, the work done in moving a \(2\) \(μC\) point charge from corner \(A\) to corner \(B\) of a square \(ABCD\) is

[MHT-CET 2024, May 4, Shift 2]

  • (1) Zero
  • (2) \(5\)
  • (3) \(2\)
  • (4) \(20\)


24. If a unit charge is taken from one point to another point over an equipotential surface, then

[MHT-CET 2024, May 10, Shift 2]

  • (1) Work is done on the charge 
  • (2) Work is done by the charge
  • (3) Work done on the charge is constantly increasing
  • (4) Work done to move a charge is zero


25. Three charges are placed at the vertices of an equilateral triangle as shown in the figure. For what value of charge ‘\(Q\)’, the electrostatic potential energy of the system is zero?

[MHT-CET 2024, May 2, Shift 1]

  • (1) \(-q\)
  • (2) \( \frac{q}{2}\)
  • (3) \(-2q\)
  • (4) \( - \frac{q}{2}\)


26. Two point charges \(q_1\)=\(6\) \(μC\) and \(q_2\) = \(4\) \(μC\) are kept at points \(A\) and \(B\) in air where \(AB\) = \(10\) \(cm\). What is the increase in potential energy of the system when \(q_2\) is moved toward \(q_1\) by \(2cm\) ?  [\( \frac{1}{4π∈_0} \) = \(9\) x \(10^9\) SI unit]

[MHT-CET 2024, May 10 ,Shift 1]

  • (1) \(0.27\) \(J\)
  • (2) \(0.54\) \(J\)
  • (3) \(0.81\) \(J\)
  • (4) \(54\) \(J\)

 

27. The electric potential at a point on the axis of an electric dipole is proportional to [ \(r\) = distance between centre of the electric dipole and the point]

[MHT-CET 2024, May 10, Shift 2]

  • (1) \( \frac{1}{r}\)
  • (2) \( \frac{1}{r^2}\)
  • (3) \( r\)
  • (4) /\( 1 r^3\)


28. An electric dipole of moment \( \vec{P} \) is lying along a uniform electric field \( \vec{E} \) . The work done in rotating the dipole through \( \frac{π^C}{3}\) is [sin 30º = cos 60º = 0.5, cos 30º = sin 60º = \( \sqrt{3} \) / \(2\) ]

[MHT-CET 2024, May 3, Shift 1]

  • (1) \(3\) \( pE\)
  • (2) \( \sqrt{2} \) \( pE\)
  • (3) \( pE\)
  • (4) \( \frac{pE}{2} \)


29. An electric dipole will have minimum potential energy when it subtends an angle  \begin{bmatrix} \cos 0^\circ = 1 \\ \sin 0^\circ = 0 \end{bmatrix} \begin{bmatrix} \cos 90^\circ = 0 \\ \cos \pi = -1 \end{bmatrix}

[MHT-CET 2024, May 11, Shift 2]

  • (1) \(π\) with direction of field
  • (2) \( \frac{π}{2} \) with direction of field
  • (3) \( \frac{3π}{2} \) with direction of field
  • (4) zero with direction of field


30. A small particle carrying a negative charge of \(1.6\) × \(10^{–16}\) \(C\)  is suspended in equilibrium between two horizontal metal plates \(8\) \(cm\) apart having a potential difference of \(980\) \(V\) across them. The mass of the particle is [\(g\) = \(9.8\) \(m/{s^2}\)]

[MHT-CET 2024, May 11, Shift 1]

  • (1) \(2\) ×  \(10^{–16}\) \(kg\) 
  • (2) \(2.2\) × \(10^{–16}\) \(kg\) 
  • (3) \(20\) × \(10^{–16}\) \(kg\) 
  • (4) \(4 \) × \(10^{–16}\) \(kg\) 


31. A particle ‘\(A\)’ has charge ‘\(+q\)’ and a particle ‘\(B\)’ has charge ‘\(+4q\)’. Each has same mass ‘\(m\)’. When they are allowed to fall from rest through the same potential, the ratio of their speeds will become (particle \(A\) to particle \(B\))

[MHT-CET 2024, May 11, Shift 2]

  • (1) \({2 : 1}\)
  • (2) \({1 : 2}\)
  • (3) \({1 : 4}\)
  • (4) \({4 : 1}\)


32. An electron of mass ‘\(m\)’ and charge ‘\(q\)’ is accelerated from rest in a uniform electric field of intensity ‘\(E\)’. The velocity acquired by it as it travels a distance ‘\(l\)’ is ‘\(v\)’. The ratio \( \frac{q}{m} \) in terms of \(E\), \(l\) and \(v\) is 

[MHT-CET 2024, May 4, Shift 2]

  • (1) \( \frac{v^2}{2El} \)
  • (2) \( \frac{v^2 l}{2E} \)
  • (3) \( \frac{2E}{v^2 l} \)
  • (4) \( \frac{v^2 l}{E} \)

 

33. A uniformly charged conducting sphere of diameter \(14cm\) has surface charge density of \(40\) μ\(C\)\(m^{–2}\). The total electric flux leaving the surface of the sphere is nearly 
(Permittivity of free space = \(8.85\) × \(10^{–12}\) SI unit)  

[MHT-CET 2024, May 2, Shift 1]

  • (1) \(40\) \(kWb\)
  • (2) \(140\) \(kWb\)
  • (3) \(240\) \(kWb\)
  • (4) \(280\) \(kWb\)

 

34.  The electric flux over a sphere of radius ‘\(r\)’ is '\( \oint \)'. If the radius of the sphere is doubled without changing the charge, the flux will be  

[MHT-CET 2024, May 9, Shift 2]

  • (1) \(4\oint\)
  • (2) \(2\oint\)
  • (3) \( \oint \)
  • (4) \( \frac{\oint}{2} \)

 

35. A spherical rubber balloon carries a charge, uniformly distributed over the surface. As the balloon is blown up and increases in size, the total electric flux coming out of the surface 

[MHT-CET 2024, May 4, Shift 2]

  • (1) becomes zero
  • (2) decreases 
  • (3) increases 
  • (4) remains unchanged

 

36. Two surfaces \(A\) and \(B\) are enclosing the charges as shown below. The total normal electric induction (\(T. N. E. I.\)) through the surfaces \(A\) and \(B\) are respectively  

[MHT-CET 2024, May 4, Shift 2]

  • (1) \(+2q\) and \(+2q\)
  • (2) \(+q\) and \(+3q\)
  • (3) \(+q\) and \(+2q\)
  • (4) \(+2q\) and \(+3q\)

 

37. If the electric flux entering and leaving an enclosed surface is \(ϕ_1\) and \(ϕ_2\), then charge enclosed in the surface is (\(\epsilon_0\) = permittivity of free space) 

[MHT-CET 2024, May 4, Shift 2][MHT-CET 2024, May 9, Shift 1]

  • (1) \( \frac{ϕ_2-ϕ_1}{\epsilon_0} \)
  • (2) \( \frac{ϕ_2+ϕ_1}{\epsilon_0} \)
  • (3) \( \frac{ϕ_1-ϕ_2}{\epsilon_0} \)
  • (4) \(\epsilon_0\) (\(ϕ_1-ϕ_2\))

 

38. A hollow cylinder has charge ‘\(q\)’ \(C\) within it. If ‘\(ϕ\)’ is the electric flux associated with the curved surface \(B\), the flux linked with the plane surface \(A\) will be 

[MHT-CET 2024, May 16, Shift 2]

  • (1) \( \frac{1}{2} \) (\( \frac{q}{\epsilon_0} \) - \(ϕ\))
  • (2) \( \frac{q}{2\epsilon_0} \)
  • (3) \( \frac{ϕ}{3} \)
  • (4) \( \frac{q}{\epsilon_0} \) - \(ϕ\)

 

39. When the dielectric is placed in an external electric field, the electric field inside the dielectric is 

[MHT-CET 2024, May 16, Shift 1]

  • (1) Less than the external electric field
  • (2) Larger than the external electric field
  • (3) Equal to the external electric field
  • (4) Equal to or greater than external electric field

 

40. The function of dielectric in a capacitor is 

[MHT-CET 2024, May 9, Shift 1]

  • (1) To reduce the effective potential on plates 
  • (2) To increase the effective potential on plates
  • (3) To decreases the capacitance
  • (4) To reduce the plate area of capacitor 

 

41. A parallel plate capacitor is charged and then isolated. If the separation between the plates is increased, which one of the following statement is NOT correct? 

[MHT-CET 2024, May 3, Shift 2]

  • (1) Charge remains constant after it is isolated
  • (2) Potential difference across the plates decreases
  • (3) Potential difference across the plates increases
  • (4) Capacitance of capacitor decreases

 

42. The graph shows the variation of voltage ‘\(V\)’ across the plates of two capacitors \(A\) and \(B\) versus increase in charge ‘\(Q\)’ stored in them. Then 

 [MHT-CET 2024, May 16, Shift 2]

  • (1) \(A\) has high capacity capacitor 
  • (2) \(B\) has high capacity capacitor 
  • (3) Both have same capacity 
  • (4) Capacity of \(A\) = \(2\) times capacity of \(B\) 

 

43. Two circular metal plates each of radius ‘\(r\)’ are kept parallel to each other distance ‘\(d\)’ apart. The capacitance of the capacitor formed is ‘\(C_1\)’. If the radius of each of the plates is increased to \(\sqrt{2}\) times the earlier radius and their distance of separation decreased to half the initial value, the capacitance now becomes ‘\(C_2\)’. The ratio of the capacitances \(C_1\) : \(C_2\)’ is 

[MHT-CET 2024, May 3, Shift 1]

  • (1) \({1 : 1}\)
  • (2) \({1 : 2}\)
  • (3) \({1 : 4}\)
  • (4) \({4 : 1}\)

 

44. When three capacitors of equal capacities are connected in parallel and one more capacitor of the same capacity is connected in series with the combination, the resultant capacity is \(4.5\) \(μF\). The capacity of each capacitor is 

[MHT-CET 2024, May 11, Shift 1]

  • (1) \(5\) \(μF\)
  • (2) \(6\) \(μF\)
  • (3) \(7\) \(μF\)
  • (4) \(8\) \(μF\)

 

45.  Seven capacitors each of capacitance \(2\) \(μF\) are connected in a configuration to obtain an effective capacitance \( \frac{6}{13} \)\(μF\) . The combination which will achieve this will have 

[MHT-CET 2024, May 10, Shift 1]

  • (1) \(5\) capacitors in parallel and then \(2\) capacitors in series
  • (2) \(4\) capacitors in parallel and then \(3\) capacitors in series
  • (3) \(3\) capacitors in parallel and then \(4\) capacitors in series 
  • (4) \(2\) capacitors in parallel and then \(5\) capacitors in series 

 

46. Two parallel plate air capacitors of same capacity ‘\(C\)’ are connected in series to a battery of emf ‘\(E\)’. Then one of the capacitors is completely filled with dielectric material of constant ‘\(K\)’. The change in the effective capacity of the series combination is

[MHT-CET 2024, May 11, Shift 1]

  • (1) \( \frac{C}{2} \) [\( \frac{K+1}{K-1} \)]
  • (2) \( \frac{2}{C} \) [\( \frac{K-1}{K+1} \)]
  • (3) \( \frac{C}{2} \) [\( \frac{K-1}{K+1} \)]
  • (4) \( \frac{C}{2} \) \([ \frac{K-1}{K+1} ]^2\)

 

47. Air capacitor has capacitance ‘\(C_1\)’. The space between two plates of capacitor is filled with two dielectrics as shown in the figure. The new capacitance of the capacitor is ‘\(C_2\)’. The ratio \( \frac{C_1}{C_2} \) is (\(d\) = distance between two plates of capacitor, \(K_1\) and \(K_2\) are dielectric constants of two dielectrics respectively) 

[MHT-CET 2024, May 16, Shift 2]

  • (1) \(K_1\) + \(K_2\)
  • (2) \( \frac{K_1+K_2}{K_1-K_2} \)
  • (3) \( \frac{2K_1K_2}{K_1+K_2} \)
  • (4) \( \frac{K_1+K_2}{2K_1K_2} \)

 

48. Air capacitor has capacitance of \(1μF\). Now the space between two plates of capacitor is filled with two dielectrics as shown in figure. The capacitance of the capacitor is [ \(d\) = distance between two plates of capacitor, \(K_1\) and \(K_2\) are dielectric constants of first dielectric and second dielectric respectively]  

[MHT-CET 2024, May 9, Shift 2]

  • (1) \(3\) \(μF\)
  • (2) \(6\) \(μF\)
  • (3) \(8\) \(μF\)
  • (4) \(12\) \(μF\)

 

49. A parallel plate air capacitor, with plate separation ‘\(d\)’ has a capacitance of \(9\) \(pF\). The space between the plates is now filled with two dielectrics, the first having \(K_1\) = \(3\) and thickness \(d_1\) = \(d\)/\(3\), while the \(2^{nd}\) has \(K_2\) = \(6\) and thickness \(d_2\) = \(2d\)/\(3\). The capacitance of the new capacitor is 

[MHT-CET 2024, May 4, Shift 1]

  • (1) \(3.8\) \(pF\)
  • (2) \(20.25\) \(pF\)
  • (3) \(40.5\) \(pF\)
  • (4) \(45\) \(pF\)

 

50. A parallel plate capacitor has plate area \(40\) \(cm^2\) and plate separation \(2\) \(mm\). The space between the plates is filled with a dielectric medium of thickness \(1\) \(mm\) and dielectric constant \(5\). The capacitance of the system is (\(\epsilon_0\) = permitity of vaccum) 

[MHT-CET 2024, May 4, Shift 1]

  • (1) \(24\) \(\epsilon_0F\)
  • (2) \( \frac{3}{10} \) \(\epsilon_0F\)
  • (3) \( \frac{10}{3} \) \(\epsilon_0F\)
  • (4) \(10\) \(\epsilon_0F\)

 

51. In the circuit shown in the following figure, the potential difference across \(3\) \(μF\) capacitor is 

[MHT-CET 2024, May 15, Shift 2]

  • (1) \(4\) \(V\)
  • (2) \(6\) \(V\)
  • (3) \(10\) \(V\) 
  • (4) \(16\) \(V\) 

 

52. A series combination of \(n_1\) capacitors, each of value \(C_1\) is charged by a source of potential difference 6\(V\). Another parallel combination of \(n_2\) capacitors, each of value \(C_2\) is charged by a source of potential difference 2\(V\). Total energy of both the combinations is same. The value of \(C_2\) in terms of \(C_1\) is  

[MHT-CET 2024, May 16, Shift 1]

  • (1) \( \frac{3C_1}{n_1n_2} \)
  • (2) \( \frac{9n_2}{n_1} \) \(C_1\)
  • (3) \( \frac{3n_2}{n_1} \) \(C_1\)
  • (4) \( \frac{9C_1}{n_1n_2} \)

 

53. The potential difference that must be applied across the series and parallel combination of \(4\) identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is 

[MHT-CET 2024, May 9, Shift 2]

  • (1) \({1 : 2}\)
  • (2) \({1 : 4}\)
  • (3) \({4 : 1}\)
  • (4) \({2 : 1}\)

 

54. Two identical capacitors \(A\) and \(B\) are connected in series to a battery of E.M.F. ‘\(E\)’. Capacitor \(B\) contains a slab of dielectric constant \(K\). \(Q_A\) and \(Q_B\) are the charges stored in \(A\) and \(B\). When the dielectric slab is removed, the corresponding charges are \(Q'_A\) and \(Q'_B\) . Then

[MHT-CET 2024, May 16, Shift 1]

  • (1) \( \frac{Q'_A}{Q_A} \) = \( \frac{K}{2} \)
  • (2) \( \frac{Q'_B}{Q_B} \) = \( \frac{K+1}{2} \)
  • (3) \( \frac{Q'_A}{Q_A} \) = \( \frac{K+1}{K} \)
  • (4) \( \frac{Q'_B}{Q_B} \) = \( \frac{K+1}{2k} \)

 

55.  A parallel plate capacitor of capacitance ‘\(C\)’ is connected to a battery and charged to a potential difference ‘\(V\)’. Another capacitor of capacitance \(3C\) is similarly charged to a potential difference \(3V\). The charging battery is then disconnected and capacitors are connected in parallel to each other in such a way that positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is  

[MHT-CET 2024, May 9, Shift 1]

  • (1) \( \frac{3}{2} \)\(CV^2\)
  • (2) \(8CV^2\)
  • (3) \( \frac{13}{2} \)\(CV^2\)
  • (4) \(18CV^2\)

 

56. Two identical capacitors have the same capacitance ‘\(C\)’. One of them is charged to potential \(V_1\) and other to \(V_2\). The negative ends of capacitors are connected together. When positive ends are also connected, the decrease in energy of the combined system is  

[MHT-CET 2024, May 10, Shift 1]

  • (1) \( \frac{1}{4} \)\(C\) \((V_1^2+V_2^2)\)
  • (2) \( \frac{1}{4} \)\(C\) \((V_1^2-V_2^2)\)
  • (3) \( \frac{1}{4} \)\(C\) \((V_1+V_2)^2\)
  • (4) \( \frac{1}{4} \)\(C\) \((V_1-V_2)^2\)

 

57. The van de Graaff Generator is not based on  

[MHT-CET 2024, May 3, Shift 2]

  • (1) The phenomenon of Corona Discharge in X-ray tube 
  • (2) The application of electric field and magnetic field which are perpendicular to each other
  • (3) The property that charge given to a hollow conductor is transferred to its outer surface and distributed uniformly over it
  • (4) The fact that a charge is continuously supplied to an isolated metallic conductor, the potential of the conductor goes on increasing

 

We post the solution to this paper in 24 hours. The download link will be activated at that time. In the meantime, students are encouraged to attempt the questions on their own and use the comments section to discuss and collaborate with each other.

Download solution here.

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