A simple pendulum oscillating in air has peri | 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 $T = 2\pi \sqrt{\frac{L}{g_{	ext{eff}}}}.$ In air,the effective acceleration due to gravity is $

Vedclass · Accepted Answer

$4T\sqrt{\frac{1}{15}}$

Vedclass · Answer

(B) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{L}{g_{	ext{eff}}}}.$ In air,the effective acceleration due to gravity is $g_{	ext{eff}} = g.$ So,$T = 2\pi \sqrt{\frac{L}{g}}.$ When the bob is immersed in a liquid of density $ho_l$ and the bob has density $ho_b,$ the effective acceleration due to gravity $g'$ is given by $g' = g \left( 1 - \frac{ho_l}{ho_b} ight).$ Given $ho_l = \frac{1}{16} ho_b,$ we have $g' = g \left( 1 - \frac{1}{16} ight) = g \left( \frac{15}{16} ight).$ The new time period $T'$ is $T' = 2\pi \sqrt{\frac{L}{g'}} = 2\pi \sqrt{\frac{L}{g \cdot \frac{15}{16}}}.$ Simplifying this,$T' = 2\pi \sqrt{\frac{L}{g}} \cdot \sqrt{\frac{16}{15}} = T \cdot \frac{4}{\sqrt{15}} = 4T \sqrt{\frac{1}{15}}.$

$A$ simple pendulum oscillating in air has period $T.$ The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is $\frac{1}{16}$ of the material of the bob. If the bob is inside the liquid all the time,its period of oscillation in this liquid is:

Similar Questions

The angular amplitude of a simple pendulum is $\theta_0$. The maximum tension in its string will be

The graph between the time period $(T)$ and the length $(l)$ of a simple pendulum is

If a body dropped freely from a height of $20 \,m$ reaches the surface of a planet with a velocity of $31.4 \,ms^{-1}$, then the length of a simple pendulum that ticks seconds on the planet is (in $\,m$)

The average speed of the bob of a simple pendulum oscillating with a small amplitude $A$ and time period $T$ is

$A$ small sphere oscillates simple harmonically in a watch glass whose radius of curvature is $1.6 \ m$. The period of oscillation of the sphere is (acceleration due to gravity $g = 10 \ m/s^2$) (in $\pi \ s$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module