A wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of `15^@` in time `t` sec. Then how much it rotates in the next `2t` sec

Options

A. `90^(@)`
B. `120^(@)`
C. `30^(@)`
D. `45^(@)`

Answer

B

Explanation

If angular acceleration is constant, we have
`theta=omega_(0)t+(1)/(2)alphat^(2)`
Given, `theta=15^(@), omega_(0)=0`
For the 1st condition (time = t s)
`15^(@)=(1)/(2) alphat^(2)`….(i)
For the 2nd condition (time = 3t s)
`theta_(1)=(1)/(2)alpha(3t)^(2)=(1)/(2)(alpha)9t^(2)`....(ii)
So, the increase in angle through which it rotates in the next 2s,
`Deltatheta=theta_(1)=(1)/(2)alphat^(2)`
`=9xx(1)/(2)alphat^(2)-(1)/(2)alphat^(2)=8((1)/(2)alphat^(2))`
`=8xx15^(@) =120^(@)` [from eq. (i)].