A car wheel is rotated to uniform angular acceleration about its axis, intially its angular velocity is zero .It rotates through an angle `theta_1`in the first 2 s , in the next 2 s, it rotates through an additional angle `theta_2`,the ratio of `theta_2/theta_1` is

Options

A. 1
B. 2
C. 3
D. 5

Answer

C

Explanation

`alpha`is the uniform angular acceleration
`therefore" "theta_(1)=omega_(0)t+(1)/(2)xxt^(2)rArromega_(0)=0rArrt=2s`
`therefore " "theta_(1)=0+(1)/(2)xx4=2alpha" "....(i)`
Again," "`theta=omega_(0)t+(1)/(2)alphat^(2)rArrt=4s`
`theta=0+(1)/(2)alpha.4xx4=8alpha`
`therefore" "theta^(2)=theta-theta_(1)=8alpha-2alpha=6alpha" "....(ii)`
and `(theta_(2))/(theta_(1))=(6alpha)/(2alpha)=3`