A car is moving with a constant speed. The wheels of the car make 120 rotations per minute. The brakes are applied and the car comes to rest in 8 second. How many rotations are completed by the wheels, before the car is brought to rest? (Assume that the brakes produce a constant retarding force)

Options

A. 4
B. 6
C. 8
D. 10

Answer

C

Explanation

`omega_(0)=2pin_(0)=2pixx(120)/(60)=4pi" rad/s"`
`because omega=omega_(0)+alphat" "therefore 0=4pi+8alpha`
`therefore" "alpha=-(4pi)/(8)=(pi)/(2)" rad/s"^(2)" (It is retardation.)"`
The total angle described in 8 second is
`theta =omega_(0)t+(1)/(2)alphat^(2)`
`=4pixx8-(1)/(2)xx(pi)/(2)xx64=32pi-16pi=16pi`
`therefore" No. of rotations n"=(16pi)/(2pi)=8`