Kelvi

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is:

medium

Oscillations

2024

physics

$2\sqrt{3}$

$\sqrt{3}$

Explanation

To solve this problem, we need to understand how the time period of a simple pendulum is affected by changes in mass and length. $\\$ The time period $T$ of a simple pendulum is given by the formula: $\\ T = 2\pi \sqrt{\frac{L}{g}} \\$

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If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x2 \frac{x}{2} 2x​ times its original time period. Then the value of x x x is:

Explanation

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If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is: