Question

A shaft rotating at 1725 rpm is brought to rest uniformly in the 20s. The number of revolutions that the shaft will make during this time is
$
  (a){\text{ 1680}} \\
  (b){\text{ 575}} \\
  (c){\text{ 287}} \\
  (d){\text{ 627}} \\
$

Answer 1

Hint – In this question use the basic concept that rpm stands for rotation per minute, so 1725 rpm depicts that the shaft is rotating at 1725 rotations per unit. Use the basic unitary method to compute the shaft’s rotation for 20 sec. This will help approaching the problem.
Step by step answer:
Initial rotation of the shaft = 1725 rpm.
Rpm = revolutions per minute
I.e. in 1 minute the shaft rotates 1725 times.
Now as we know that 1 min = 60 sec.
So in 60 seconds the shaft rotates 1725 times.
Now it is given that the shaft is brought to rest uniformly in 20 seconds.
So we have to calculate how many times the shaft rotates.
So in 1 sec shaft rotates (1725/60) times.
So in 20 seconds the shaft rotates $\dfrac{{1725}}{{60}} \times 20$ times.
Now simplify this we have,
$ \Rightarrow \dfrac{{1725}}{{60}} \times 20 = \dfrac{{1725}}{3} = 575$ times.
Therefore in 20 sec in which the shaft comes to rest rotates 575 times.
So this is the required answer.
Hence option (B) is the correct answer.

Note – The basic conversion that $1\min = 60\sec $ helps in carrying out the calculations of evaluation of rotation of shaft in 1sec, since 1 sec can be taken out thus by simple multiplication of 20sec to these number of rotation will help finding the number of rotations for 20sec. This forms the basis of the unitary method that first finds the unknown for 1sec and then evaluates it for any x sec asked. There is always a minor confusion between the concepts of rotation of revolution. Rotation is always around the axis which passes through the body itself undergoing rotation however revolution is around a body that may be stationary, undergoing rotation or undergoing revolution around another body.