JEE Main 2026 — Jan 22, Shift 1 — Physics solution

JEE Main2026Jan 22, Shift 1Physics

A simple pendulum has a bob with mass $m$ and charge $q$ . The pendulum string has negligible mass. When a uniform and horizontal electric field $E$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is _____.

(g : acceleration due to gravity)

A
$m g - q E$
B
$m g + q E$
C
$m^{2} g^{2} + q^{2} E^{2}$
D
$m^{2} g^{2} - q^{2} E^{2}$

Solution

At equilibrium, three forces act on the bob: gravity $m g$ (down), electric force $q E$ (horizontal), and string tension $T$ along the string.

The string must be aligned with the resultant of the gravitational and electric forces (otherwise there’d be an unbalanced tangential component). Since the gravitational and electrical forces are perpendicular, their resultant has magnitude $(m g)^{2} + (q E)^{2}$ .

The tension balances this resultant: $T = m^{2} g^{2} + q^{2} E^{2}$ .

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