A simpel pendulum is vibrating with an angular amplitdue of as shown in figure, then:

Options

A. `theta = 0`, acceleration directed downward
B. `theta = 0`,acceleration directed upward
C. `theta = 90^@`, acceleration directed downward
D. `theta= cos^(-1)(1/(sqrt(3)))`,acceleration directed horizontal

Answer

B, C, D

Explanation

At `theta = 90^@ , v = 0`,
`:. a_(n) = (v^2)/r = 0 and a_(t) = g sin 90^@ = g`
At any angular position `theta, h = 1 cos theta " ":. " "v^2 = 2 ghI`
`a_(n) = (v^2)/r = (2 gl cos theta)/(l) = 2 g cos theta and a_(t) = g sin theta`
Thus `tan theta = (a_x)/(a_t) " or "(sin theta)/(cos theta) = (2 g cos theta)/(g sin theta) " or " 2 cos^2 theta = sin^2 theta = 1 - cos^2 theta`
`cos theta = 1/(sqrt(3))`