Question

A wheel is subjected to uniform angular acceleration about its axis. Initially, its angular velocity is zero. In the first `2 sec`, it rotates through an angle `theta_(1)`, in the next `2 sec`, it rotates through an angle `theta_(2)`. The ratio of `theta_(2)//theta_(1)` is
A. `1`
B. `2`
C. `3`
D. `5`

Answer 1

Correct Answer - C
For first `2` seconds
`theta_(1) = omega_(0) + (1)/(2)alpha (t)^(2), as omega_(0) = 0`
`:. theta_(1) = (1)/(2)alpha (2)^(2) = 2 alpha`
for next two second
`(theta_(1) + theta_(2)) = omega_(0)t + (1)/(2)alpha t^(2)`
`2 alpha + theta_(2)alpha (4)^(2) = 8 alpha`
`theta_(2) = 6 alpha or (theta_(2))/(theta_(1)) = (6 alpha)/(2 alpha) = 3`