Question

The speed of the tip of second’s hand of a watch of length $1.5\,cm$ is
A. ${\text{0}}{\text{.025}}\,{\text{cm/s}}$
B. ${\text{0}}{\text{.05}}\,{\text{cm/s}}$
C. ${\text{0}}{\text{.16}}\,{\text{cm/s}}$
D. ${\text{1}}\,{\text{cm/s}}$

Answer 1

Hint:The magnitude of a change in an object's location determines its speed; it is thus a scalar quantity. The average speed of an object in a given time period is equal to the object's distance travelled divided by the interval's length.

Complete step by step answer:
The dimensions of speed are distance divided by time. The metre per second is the SI unit of time, but the kilometre per hour is the most commonly used unit in daily life. The knot is widely used in air and marine transport. We know that the second hand completes one rotation in $60$ seconds.
Hence, ${\text{t}}\,{\text{ = }}\,{\text{60}}\,{\text{sec}}$
Distance covered $ = \,2\pi r$
The length of the seconds hand will be the radius.
We are given that, ${\text{r}}\,{\text{ = }}\,{\text{1}}{\text{.5}}$
The speed of the tip of second’s hand of a watch is given by,
Speed = $\dfrac{{{\text{distance}}}}{{{\text{time}}}}$
\[{\text{V}}\,{\text{ = }}\,\dfrac{{{{2\pi r}}}}{{\text{t}}}\]
Substituting the values in the above equations we get,
$V\, = \,\dfrac{{2\pi \, \times \,1.5}}{{60}}$
On further solving, we get
\[{\text{V}}\,{\text{ = }}\,{\text{0}}{\text{.}}\,{\text{157}}\, \approx \,{\text{0}}{\text{.16}}\,{\text{cm/sec}}\]
Hence, the speed of the tip of second’s hand of a watch of length $1.5\,cm$ is ${\text{0}}{\text{.16}}\,{\text{cm/s}}$.

So, the correct option is C.

Note:A speedometer is a device that shows the speed of a vehicle and is commonly used in conjunction with an odometer to monitor the distance travelled. An early type of speedometer, which was normally fitted to locomotives, is credited to Charles Babbage. A revolving flexible cable connected to the output of the vehicle's transmission is used to drive the speedometer.