Question

The wheel of a motor, accelerated uniformly from rest, rotates through $2.5$ radian during first second, find the angle rotates during next second

• A. $5$ rad
• B. $7.5$ rad
• C. $3.5$ rad
• D. $10$ rad

Answer 1

The correct option is B $7.5$ rad

$\theta =\omega ₀t+\frac{1}{2}\alpha t^2$

given:

$\theta =2.5rad$

$\omega ₀=0;$

$t=1sec;$

$\alpha =?$

using this values we get

$⟹2.5=0\times t+\frac{1}{2}\alpha 1^2$

$⟹\alpha =2\times 2.5$

$⟹\alpha =5rad/s^2$

Angle turned during the first $2se{c}^2$:

$\frac{1}{2}\alpha t^2=\frac{1}{2}\times 5\times 2^2=10rad$

Angle turned during the 2nd second$=10rad-2.5rad=7.5rad.$