Q.1.A pendulum clock keeping correct time is taken to high altitudes,its length should be decreased to keep correct time.Why?
Q.2.A simple pendulum has a hollow bob filled with a liquid of density d.If the liquid drains out of a small hole in the bottom of the bob,then frequency of oscillations first decreases and then increases.Why?
Q.3.The position vector of a particle from the origin is given by
r=A(i^coswt+j^sinwt). the motion is on circle.Why?
1. smaller g because further from center of gravity of earth.
2. At first as the liquid drops out of the top of the sphere, the center of mass of the sphere moves down making the effective length of the pendulum longer. Then as the fluid drains out of the bottom half of the sphere the center of the pendulum mass again shortens to the center of the sphere.
3.x and y components
rx = A cos wt
ry = A sin wt
|r| = sqrt (rx^2 + ry^2)
|r| = sqrt (A^2 cos^2 wt + A^2 sin^2 wt)
but cos^2 + sin^2 = 1
so
r = A constant radius