If the mass of the bob in a simple pendulum i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{\ell}{g}}$,where $\ell$ is the length of the pendulum and $g$ is the accel

Vedclass · Accepted Answer

$\sqrt{2}$

Vedclass · Answer

(A) The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{\ell}{g}}$,where $\ell$ is the length of the pendulum and $g$ is the acceleration due to gravity. The time period is independent of the mass of the bob.Given that the new length $\ell^{\prime} = \frac{\ell}{2}$.The new time period $T^{\prime} = 2 \pi \sqrt{\frac{\ell^{\prime}}{g}} = 2 \pi \sqrt{\frac{\ell}{2g}} = \frac{1}{\sqrt{2}} \left( 2 \pi \sqrt{\frac{\ell}{g}} \right) = \frac{1}{\sqrt{2}} T$.According to the problem,$T^{\prime} = \frac{x}{2} T$.Therefore,$\frac{x}{2} = \frac{1}{\sqrt{2}}$.$x = \frac{2}{\sqrt{2}} = \sqrt{2}$.

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

Similar Questions

$A$ simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum,its acceleration vector $\vec a$ is correctly shown in

$A$ hollow pendulum bob filled with water has a small hole at the bottom through which water escapes at a constant rate. Which of the following statements describes the variation of the time period $T$ of the pendulum as the water flows out?

$Assertion:$ The time period of a simple pendulum on a satellite orbiting the Earth is infinity.
$Reason:$ The time period of a simple pendulum is inversely proportional to $\sqrt{g}$.

$A$ simple pendulum of period $T$ has a metal bob which is negatively charged. If it is allowed to oscillate above a positively charged metal plate,its period will

If a simple pendulum can reach a height of $10 \ cm$,what is its velocity when it is at its mean position (in $m/s$)? $(g = 9.8 \ m/s^2)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module