One degree is
60 minutes
Understanding Angular Measurement: Degrees to Minutes
Angular measurement is a way to quantify angles. The most common unit is the degree ($^\circ$). A full circle is divided into 360 degrees.
The Degree-Minute-Second System
Just like time is measured in hours, minutes, and seconds, angles can also be broken down into smaller units:
- Minutes of arc ($'$): Each degree is divided into 60 smaller units called minutes.
- Seconds of arc ($''$): Each minute is further divided into 60 seconds.
This system helps in precisely measuring angles, especially in fields like astronomy and navigation.
Conversion Factors
The fundamental relationship between degrees and minutes is:
$$1^\circ = 60'$$
Similarly, the relationship between minutes and seconds is:
$$1' = 60''$$
To convert degrees directly to seconds, you multiply by both factors:
$$1^\circ = 1^\circ \times \frac{60'}{1^\circ} \times \frac{60''}{1'} = 3600''$$
Analyzing the Options
Let's look at the provided options in light of these definitions:
| Option Text | Equivalence | Correct? |
|---|---|---|
| 60 seconds | $1' = 60''$ | No (This is the value of 1 minute, not 1 degree) |
| 60 minutes | $1^\circ = 60'$ | Yes |
| 100 seconds | Incorrect conversion | No |
| 100 minutes | Incorrect conversion | No |
Therefore, one degree is equivalent to 60 minutes of arc.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
