JEE MAIN - Physics (2024 - 30th January Evening Shift - No. 27)
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $$37^{\circ}$$ with each other. When suspended in a liquid of density $$0.7 \mathrm{~g} / \mathrm{cm}^3$$, the angle remains same. If density of material of the sphere is $$1.4 \mathrm{~g} / \mathrm{cm}^3$$, the dielectric constant of the liquid is _______ $$\left(\tan 37^{\circ}=\frac{3}{4}\right)$$
Answer
2
Explanation
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$$\begin{aligned} & T \cos \theta=m g \\ & T \sin \theta=F_e \\ & \tan \theta=\frac{F_e}{m g} \end{aligned}$$
$$\tan \theta=\frac{F_c}{\rho_B V g}$$ ..... (i)
$$\tan \theta=\frac{F_e}{\frac{k}{\left(\rho_B-\rho_L\right) V g}}$$ ..... (ii)
From Eq. (i) & (ii)
$$\begin{aligned} & \rho_{\mathrm{B}} \mathrm{Vg}=\left(\rho_{\mathrm{B}}-\rho_{\mathrm{L}}\right) \mathrm{kVg} \\ & 1.4=0.7 \mathrm{k} \\ & \mathrm{k}=2 \end{aligned}$$
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