Q27 of 37 Page 23

If |A| = 2 and |B| = 4, then match the relations in column I with the angle θ between A B and in column II.

Given:


|A| = 2, |B| = 4.


(a)


So,


So, θ = 90°


Option (a) matches with (ii)


(b)


So,


So, θ = 0°


Option (b) matches with (i)


(c)


So,


So, θ = 60°


Option (c) matches with (iv)


(d)


So,


So, θ = 180°


Option (d) matches with (iii)


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25

(a) Earth can be thought of as a sphere of radius 6400 km. Any object (or a person) is performing circular motion around the axis of earth due to earth’s rotation (period 1 day). What is acceleration of object on the surface of the earth (at equator) towards its centre? what is it at latitude θ? How does these accelerations compare with g = 9.8 m/s2?

(b) Earth also moves in circular orbit around sun once every year with on orbital radius of 1.5 X 1011 m. What is the acceleration of earth (or any object on the surface of the earth) towards the centre of the sun? How does this acceleration compare with g = 9.8 m/s2?


(Hint : acceleration = )


 26

Given below in column I are the relations between vectors a, b and c and in column II are the orientations of a, b and c in the XY plane. Match the relation in column I to correct orientations in column II.

Column I


(a) a + b = c


(b) a – c = b


(c) b – a = c


(d) a + b + c = 0


Column II






 28

If |A|= 2 and |B| = 4, then match the relations in column I with the angle θ between A and B in column II

 29

A hill is 500 m high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of 125 m/s over the hill. The canon is located at a distance of 800m from the foot of hill and can be moved on the ground at a speed of 2 m/s; so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach on the ground across the hill? Take g =10 m/s2.