Question

Which among the following statement is incorrect?
I. The angle between two consecutive digits in a clock is $30^{\circ}$.
II. The minute hand rotates through an angle of $6^{\circ}$ in a minute.
III. The hour hand rotates through an angle of $30^{\circ}$ in one hour i.e., $(1 / 2)^{\circ}$ in a minute.
IV. The second hand rotates through an angle of $180^{\circ}$ in a minute.

• A. I is incorrect
• B. II is incorrect
• C. III is incorrect
• D. IV is incorrect

Answer 1

Answer: (D)

The number of digits in a clock is 12 .
So, the angle between two consecutive digits in a clock is
$=\frac{360^{\circ}}{12}=30^{\circ}$
or $\frac{\pi}{6}$ radian.
The minute hand rotates through $360^{\circ}$ in $60 \min$.
So, in $1 \min$ it rotates through $\frac{360^{\circ}}{60}=6^{\circ}$.
The hour hand rotates through $360^{\circ}$ in $12\, h$.
So, in one hour it rotates through $\frac{360^{\circ}}{12}=30^{\circ}$ and in one minute it rotates through $\frac{30^{\circ}}{60}=\left(\frac{1}{2}\right)^{\circ}$. The second hand rotates through $360^{\circ}$ in a minute.
Thus, we see that option (d) is incorrect.