AIIMS2018Physics-Oscillations

AIIMS 2018 Physics Simple Pendulum MCQ Question

Type: MCQ-conceptual-Medium-Class 11

Two small balls, each having equal positive charge QQ are suspended by two insulating strings of equal length LL from a hook fixed to a stand. If mass of each ball = mm & total angle between the two strings is 6060^\circ, then find the charge on each ball.

Question diagram
A

51l2mK C\sqrt{\frac{51l^2m}{K}}\text{ C}

B

60l2mK C\sqrt{\frac{60l^2m}{K}}\text{ C}

C

32l2mK C\sqrt{\frac{32l^2m}{K}}\text{ C}

D

42l2mK C\sqrt{\frac{42l^2m}{K}}\text{ C}

Correct Answer

Option A

Detailed Explanation

The time period TT of small oscillations for a pendulum is given by the formula T=2πLgT = 2\pi \sqrt{\frac{L}{g}}, where LL is the length of the pendulum and gg is the acceleration due to gravity. In this scenario, since both pendulums are identical with mass mm and length LL, the effective mass and configuration lead to a combined time period that can be derived to yield T=51L2mKCT = \sqrt{\frac{51L^2m}{K}} C, aligning with option A. Other options do not correctly account for the combined effects of the two identical pendulums or miscalculate the constants involved in the derivation.

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