The acceleration due to gravity on the surfac | 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 $T = 2 \pi \sqrt{\frac{l}{g}}$.For the earth: $T_e = 2 \pi \sqrt{\frac{l}{g_e}} = 3.5 \; s$,where

Vedclass · Accepted Answer

$8.4$

Vedclass · Answer

(A) The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{l}{g}}$.For the earth: $T_e = 2 \pi \sqrt{\frac{l}{g_e}} = 3.5 \; s$,where $g_e = 9.8 \; m s^{-2}$.For the moon: $T_m = 2 \pi \sqrt{\frac{l}{g_m}}$,where $g_m = 1.7 \; m s^{-2}$.Taking the ratio: $\frac{T_m}{T_e} = \sqrt{\frac{g_e}{g_m}}$.$T_m = T_e 	imes \sqrt{\frac{g_e}{g_m}} = 3.5 	imes \sqrt{\frac{9.8}{1.7}}$.$T_m = 3.5 	imes \sqrt{5.7647} \approx 3.5 	imes 2.4 = 8.4 \; s$.Thus,the time period on the moon is $8.4 \; s$.

The acceleration due to gravity on the surface of the moon is $1.7 \; m s^{-2}$. What is the time period of a simple pendulum on the surface of the moon if its time period (in $s$) on the surface of the earth is $3.5 \; s$? ($g$ on the surface of the earth is $9.8 \; m s^{-2}$)

Similar Questions

The time period of a simple pendulum is $T$. If its length is increased by $21\%$,what is the percentage increase in its time period?

$A$ 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 $\pi \ s$)

Is the oscillation of a simple pendulum at the centre of the earth possible?

The metallic bob of a simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water,then the new time period is given by

Two masses $M_{A}$ and $M_{B}$ are hung from two strings of length $l_{A}$ and $l_{B}$ respectively. They are executing $SHM$ with frequency relation $f_{A}=2 f_{B}$,then the relation is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module