A pendulum has a period of 1.8 s.
a) Its mass is doubled. What is its period now?
b) Its length is doubled. What is its period now?
The original pendulum is taken to a planet where g = 16 m/s2.
c) What is its period on that planet?
You should be able to figure these out yourself using the formula for the Period:
P = 2 pi*sqrt(L/g)
Note that it does not depend upon the mass of the pendulum.
really?? but how would i find L?
If you double L (the length), P increases by a factor sqrt2 = 1.414, no matter what L is.
(a) time period is independent of mass. so time period of pendulum remains same.
(b)
let initial time period be t1 when length is l and t2 be time period after double of length,i,then
t1=sqrt(l/g)....(1)
t2=sqrt(2l/g)
=root 2xsqrt(l/g)....(2)
from 1 and 2,
t2=root 2 times t1
where t1=1.8 s
(c)ti/t2=sqrt(g'/g)
where g=9.8m/s,ti=1.8s and g'=16m/s
solve n u will get answer
To answer these questions, we need to use the equations that relate the period of a pendulum with its other properties.
a) When the mass of a pendulum is doubled, its period is not affected. This is because the period of a pendulum is independent of its mass. Therefore, the period remains 1.8 s.
b) When the length of a pendulum is doubled, its period changes. The equation for the period of a simple pendulum is given by:
T = 2π√(L/g)
Where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
Since we doubled the length of the pendulum, the new length would be 2L. Plugging this into the equation, we get:
T' = 2π√(2L/g)
To find the new period, we substitute the given values:
T' = 2π√(2L/9.8)
c) When we take the original pendulum to a planet with a different acceleration due to gravity, we need to adjust the equation. Instead of using the acceleration due to gravity on Earth (9.8 m/s^2), we need to use the acceleration due to gravity on the new planet, g' (which is given as 16 m/s^2 in this case).
Using the same equation as before:
T' = 2π√(L/g')
Plugging in the values:
T' = 2π√(L/16)
This gives us the new period on the planet where g = 16 m/s^2.