Tag: physics

In order to make vectors a + b + c + d = 0, it is not necessary to have all the four given vectors to be null vectors. There are many other combinations which can give the sum zero.

Simple example:- a=î,b=2î,c=–3î,d=0

(b) Correct
a + b + c + d = 0
a + c = – (b + d)
Taking modulus on both the sides, we get:
| a + c | = | –(b + d)| = | b + d |
Hence, the magnitude of (a + c) is the same as the magnitude of (b + d).

(c) Correct
a + b + c + d = 0
a = – (b + c + d)
Taking modulus both sides, we get:
| a | = | b + c + d |
| a |  ≤  | a | + | b | + | c |  …. (#)

Equation (#) shows that the magnitude of a is equal to or less than the sum of the magnitudes of b, c, and d.
Hence, the magnitude of vector a can never be greater than the sum of the magnitudes of b, c, and d.

(d) Correct
For a + b + c + d = 0
a + (b + c) + d = 0
The resultant sum of the three vectors a, (b + c), and d can be zero only if (b + c) lie in a plane containing a and d, assuming that these three vectors are represented by the three sides of a triangle.

If a and d are collinear, then it implies that the vector (b + c) is in the line of a and d. This implication holds only then the vector sum of all the vectors will be zero.

This is the explanation of correct solution.

Mean solar day is the time interval between two successive noon when sun passes through zenith point (meridian).

Time taken by light to reach the earth from the sun is, 

Most of the planets orbit the Sun very near the same plane in which the Earth orbits, the ecliptic.
The orbits of the planets are ellipses with the Sun at one focus, though all except Mercury are very nearly circular. The orbits of the planets are all more or less in the same plane (called the ecliptic and defined by the plane of the Earth's orbit). The ecliptic is inclined only 7 degrees from the plane of the Sun's equator.
Hence, the statement is true.

Jupiter revolves or orbits around the Sun once every 11.86 Earth years, or once every 4,330.6 Earth days. Jupiter travels at an average speed of 29,236 miles per hour or 47,051 km per hour in its orbit around the Sun.
Hence, the planet Jupiter takes 12 years to go around the Sun.

The distance between the sun and the earth is $149,600,000 km$ which is approximately equal to $150$ million kilometers.

A solar day is the time it takes for the Earth to rotate about its axis so that the Sun appears in the same position in the sky, which is equal to $24\ hr\ 03\ min\ 55\ s$, i.e. in total, $86636\ seconds$.

Sun is regarded as the chief of solar system. It is because all of the other planets circle around it due to the gravitational pull because of its enormous mass.

The mean distance between the Earth and Sun as well as the distances within the solar system is represented by astronomical units.
One astronomical unit (AU) represents:
1 AU = 149,597,870.700 kilometers (or 149,597,870,700 meters)
An astronomical unit is the mean distance between the Earth and the Sun.