Rohan studies science from 6 PM to 7:30 PM at home. Consider the tip of the minute’s hand. Class 9
Rohan studies science from 6 PM to 7:30 PM at home. Consider the tip of the minute’s hand. Class 9
Question 1.
Rohan studies science from 6 PM to 7:30 PM at home. Consider the tip of the minute’s hand of the wall clock. During the given time interval, what is its: (i) distance travelled, (ii) displacement, (iii) speed, and (iv) velocity. The length of the minute’s hand is 7 cm. Class 9
Answer:
Given:
- Length of minute's hand (radius), R = 7 cm
- Time interval = 6:00 PM to 7:30 PM = 90 minutes = 5400 s
In 60 minutes, the minute's hand completes 1 full revolution. In 90 minutes, it completes 1.5 revolutions (1 1/2 rounds).
Part (i): Distance travelled The minute's hand tip moves along the circumference of a circle with radius 7 cm.
Circumference = 2πR
= 2 × (22/7) × 7
= 2 × 22 = 44 cm
In 1 complete revolution, distance = 44 cm. In 1.5 revolutions, distance = 1.5 × 44 = 66 cm
Part (ii): Displacement
At 6:00 PM, the minute's hand is pointing at 12 (top of the clock). After 90 minutes (1.5 revolutions), the minute's hand is pointing at 6 (bottom of the clock).
The displacement is the straight-line distance from the tip's initial position (at 12, i.e., directly above the centre) to its final position (at 6, i.e., directly below the centre).
Initial position of tip: top of the clock, at 7 cm above the centre. Final position of tip: bottom of the clock, at 7 cm below the centre.
Straight-line distance between these two points = 7 + 7 = 14 cm
Direction: from the 12 position downward to the 6 position, i.e., 14 cm directed downward (from top to bottom of clock face).
Part (iii): Speed
Speed = total distance / time
= 66 cm/5400 s
= 66/5400 m/s
= 0.01222 cm s-1 ≈ 1.22 × 10~2 cm s-1
Converting: 0.66 m / 5400 s ≈ 1.22 × 10-4 m s-1
Part (iv): Velocity (Average velocity)
Average velocity = displacement / time
= 14 cm/5400 s
= 0.00259 cm s-1 ≈ 2.59 × 10-3 cm s-1
Direction: from the 12 o'clock position toward the 6 o'clock position (straight downward through the centre of the clock face).