A wheel has a radius 10 cm and it is coupled by a belt to another wheel of radius 30 cm. The smaller wheel increases its speed from rest at a uniform rate of rad/ sec. After how much time will the speed of larger wheel become 100 c.p.m. ?

Options

A. 2s
B. 5s
C. 10s
D. 20s

Answer

C

Explanation

Here, `r_(1)omega=r_(2)omega_(2)`,`r_(1)=10cm`. `r_(2)=30cm`.
Also `omega_(2)=(2pixx100)/(60)=(10pi)/(3)=rads^(-1)`
`omega_(1)=(r_(2)omega_(2))/(r_(1))=(30)/(10)xx(10pi)/(3)=10pirads^(-1)`.
Using `omega_(1)=omega_(0)+a`,t. we get `10pi=0+pit` or t=10secconds.