An accurate clock shows 8 oclock in the morning. Through how many degrees will the hour hand rotate by the time the clock shows 2 oclock in the afternoon?

Introduction / Context:
This is a direct question based on angles formed by the hour hand of a clock. It checks the basic fact that the hour hand moves at a constant angular speed as time passes. Such questions are straightforward but help build the foundation for more complex clock problems involving relative motion of the hour and minute hands.

Given Data / Assumptions:

• The clock is accurate.
• Initial time: 8:00 a.m.
• Final time: 2:00 p.m. on the same day.
• We are concerned only with the hour hand, not the minute hand.

Concept / Approach:
On a standard clock, the hour hand completes one full circle of 360 degrees in 12 hours. Therefore, the angular movement of the hour hand per hour is: 360 degrees / 12 hours = 30 degrees per hour. Once we know the time interval in hours, we can multiply by 30 degrees to get the total rotation of the hour hand.

Step-by-Step Solution:
Step 1: Determine the time interval. From 8:00 a.m. to 2:00 p.m. the difference is 6 hours. Step 2: Use the hourly angular movement of the hour hand. The hour hand moves 30 degrees every hour. Step 3: Compute total rotation. Total rotation = 30 degrees per hour * 6 hours. Total rotation = 180 degrees. Thus, the hour hand turns through half a circle between 8:00 a.m. and 2:00 p.m.

Verification / Alternative check:
We can check by intermediate points. At 9:00 a.m. it moves 30 degrees from 8:00, at 10:00 a.m. 60 degrees, at 11:00 a.m. 90 degrees, at 12:00 noon 120 degrees, at 1:00 p.m. 150 degrees, and at 2:00 p.m. 180 degrees. The stepwise check confirms the calculation.

Why Other Options Are Wrong:
Option a (360 degrees) would imply a full revolution, which requires 12 hours, not 6 hours. Option c (90 degrees) corresponds to only 3 hours of movement, and option d (60 degrees) corresponds to only 2 hours. Neither matches the 6 hour interval between 8:00 a.m. and 2:00 p.m.

Common Pitfalls:
A common mistake is to confuse the movement of the minute hand (which completes 360 degrees in 60 minutes) with that of the hour hand. Some students also miscount the number of hours between 8:00 a.m. and 2:00 p.m., forgetting that the time interval is 6 hours, not 4 or 5 hours. Remembering the simple rule of 30 degrees per hour for the hour hand prevents such errors.

Final Answer:
The hour hand rotates through 180 degrees between 8:00 a.m. and 2:00 p.m.