6. ⇒ (MHT CET 2023 11th May Morning Shift )

Two positively charged identical spheres separated by a distance 'd' exert some force (F) on each other when they are kept in air. If both the spheres are immersed in a liquid of dielectric constant 5 , the force experienced by each is (All other parameters are unchanged.)

A. $5 F$

B. $\frac{F}{3}$

C. $\frac{F}{4}$

D. $\frac{F}{5}$

Correct Option is (D)

The ratio of force when the medium is changed will be:

$\frac{F_{1}}{F_{2}} = \frac{1}{k}$

Here, $k = 5$ ,

Therefore, the force experience by each will be $\frac{F}{5}$ .

7. ⇒ (MHT CET 2023 11th May Morning Shift )

The bob of a simple pendulum of length ' $L$ ' has a mass ' $m$ ' and charge ' $q$ '. The pendulum is suspended between the plates of a charged parallel plate capacitor. The direction of electric field is shown in figure. The period of oscillations of the simple pendulum is (acceleration due to gravity $g > qE / m$ )

MHT CET 2023 11th May Morning Shift Physics - Electrostatics Question 10 English

A. $2 π \sqrt{\frac{L}{g}}$

B. $2 π {[\frac{L}{\frac{qE}{m} - g}]}^{\frac{1}{2}}$

C. $2 π {[\frac{L}{g - \frac{qE}{m}}]}^{\frac{1}{2}}$

D. $2 π {[\frac{L}{g + \frac{qE}{m}}]}^{\frac{1}{2}}$

Correct Option is (C)

Electric force, $F_{electric} = q E$

The effective force,

$\begin{aligned} {mg}_{eff} = mg - F_{electric} \\ g_{eff} = g - \frac{qE}{m} \end{aligned}$

The period of oscillation for a simple pendulum,

$T = 2 π \sqrt{\frac{L}{g}}$

Time period when pendulum is suspended between the plates,

$\begin{aligned} T = 2 π \sqrt{\frac{L}{g_{eff}}} \\ T = 2 π {[\frac{L}{g - \frac{qE}{m}}]}^{\frac{1}{2}} \end{aligned}$

8. ⇒ (MHT CET 2023 9th May Morning Shift )

A solid metallic sphere has a charge $+ 3 Q$ . Concentric with this sphere is a conducting spherical shell having charge $- Q$ . The radius of the sphere is ' $A$ ' and that of the spherical shell is ' $B$ '. $(B > A)$ . The electric field at a distance ' $R$ ' $(A < R < B)$ from the centre is ( $ε_{0} =$ permittivity of vacuum)

A. $\frac{Q}{2 π ε_{0} R}$

B. $\frac{3 Q}{2 π ε_{0} R}$

C. $\frac{3 Q}{4 π ε_{0} R^{2}}$

D. $\frac{4 Q}{2 π ε_{0} R^{2}}$

Correct Option is (C)

We know the electric field inside a shell is zero. So, we only consider the electric field due to the solid sphere.

$\begin{aligned} ∴ Using E = \frac{1}{4 π ε_{0}} \frac{q}{r^{2}}, we get \\ E = \frac{1}{4 π ε_{0}} \frac{(3 Q)}{R^{2}} \end{aligned}$

9. ⇒ (MHT CET 2021 21th September Evening Shift )

When a piece of polythene is rubbed with wool, a negative charge of $4 \times 10^{- 7} C$ is developed on the polythene. The number of electrons transferred from wool to polythene is $[e = 1.6 \times 10^{- 19} C]$

A. $1.5 \times 10^{12}$

B. $3.5 \times 10^{13}$

C. $2.5 \times 10^{13}$

D. $2.5 \times 10^{12}$

Correct Option is (D)

$q = 4 \times 10^{- 7}$

$q = N e$

$N = \frac{q}{e} = \frac{4 \times 10^{- 7}}{1.6 \times 10^{- 19}} = 2.5 \times 10^{12}$

10. ⇒ (MHT CET 2021 21th September Morning Shift )

' $F$ ' is the force between the two identical charged particles placed at a distance ' $Y$ ' from each other. If the distance between the charges is reduced to half the previous distance then force between them becomes

A. $\frac{F}{4}$

B. $4 F$

C. $2 F$

D. $\frac{F}{2}$

Correct Option is (B)

$\begin{aligned} F = \frac{1}{4 π ε_{0}} \cdot \frac{q^{2}}{r^{2}} \\ ∴ \frac{F_{2}}{F_{1}} = {(\frac{r_{1}}{r_{2}})}^{2} = (2)^{2} = 4 \\ ∴ F_{2} = 4 F_{1} \end{aligned}$

⇒Electrostatics