A simple pendulum of length l has a brass bob | vedclass

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

Question

(B) The time period of a simple pendulum is given by the formula $T = 2\pi \sqrt{\frac{l}{g}}$,where $l$ is the effective length and $g$ is the accele

Vedclass · Accepted Answer

$4l$

Vedclass · Answer

(B) The time period of a simple pendulum is given by the formula $T = 2\pi \sqrt{\frac{l}{g}}$,where $l$ is the effective length and $g$ is the acceleration due to gravity.From this formula,it is clear that $T \propto \sqrt{l}$.The time period is independent of the mass,size,or density of the bob.Let the initial length be $l_1 = l$ and the initial time period be $T_1 = T$.Let the new length be $l_2$ and the new time period be $T_2 = 2T$.Using the proportionality $T \propto \sqrt{l}$,we have $\frac{T_2}{T_1} = \sqrt{\frac{l_2}{l_1}}$.Substituting the values: $\frac{2T}{T} = \sqrt{\frac{l_2}{l}}$,which simplifies to $2 = \sqrt{\frac{l_2}{l}}$.Squaring both sides,we get $4 = \frac{l_2}{l}$,which implies $l_2 = 4l$.

$A$ simple pendulum of length $l$ has a brass bob attached at its lower end. Its period is $T$. If a steel bob of the same size,having a density $x$ times that of brass,replaces the brass bob and its length is changed so that the period becomes $2T$,then the new length is:

Similar Questions

From a fixed support,two small identical spheres are suspended by means of strings of length $1 \,m$ each. They are pulled aside as shown and then released. $B$ is the mean position. Then the two spheres collide

The period of a simple pendulum gets doubled when

Two simple pendulums are given: the first has a bob of mass $M_1$ and length $L_1$,and the second has a bob of mass $M_2$ and length $L_2$. Given $M_1 = M_2$ and $L_1 = 2L_2$. If the vibrational energy of both is the same,which of the following statements is correct?

$A$ pendulum has a time period $T$ in air. When it is made to oscillate in water, its time period is $\sqrt{2} T$. Then the relative density of the material of the bob of the pendulum is (neglect damping).

$A$ hydrometer executes simple harmonic motion when it is pushed down vertically in a liquid of density $\rho$. If the mass of the hydrometer is $m$ and the radius of the hydrometer tube is $r$,then the time period of oscillation is

Vedclass Test Series

Exam Paper Generator

Online Exam Module