Read each statement below carefully and state, with reasons, if it is true or false :
(a) The net acceleration of a particle in circular motion is always along the radius of
the circle towards the centre
(b) The velocity vector of a particle at a point is always along the tangent to the path
of the particle at that point
(c) The acceleration vector of a particle in uniform circular motion averaged over one
cycle is a null vector
An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900
km/h. Compare its centripetal acceleration with the acceleration due to gravity.
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a
constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and
direction of acceleration of the stone ?
A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much
high above the ground can the cricketer throw the same ball ?
The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that
a ball thrown with a speed of 40 m s-1 can go without hitting the ceiling of the hall ?
A passenger arriving in a new town wishes to go from the station to a hotel located
10 km away on a straight road from the station. A dishonest cabman takes him along
a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average
speed of the taxi, (b) the magnitude of average velocity ? Are the two equal ?
On an open ground, a motorist follows a track that turns to his left by an angle of 600
after every 500 m. Starting from a given turn, specify the displacement of the motorist
at the third, sixth and eighth turn. Compare the magnitude of the displacement with
the total path length covered by the motorist in each case.
A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P
of the park, then cycles along the circumference, and returns to the centre along QO
as shown in Fig. 3.20. If the round trip takes 10 min, what is the (a) net displacement,
(b) average velocity, and (c) average speed of the cyclist ?
Given a + b + c + d = 0, which of the following
statements are correct :
(a) a, b, c, and d must each be a null vector,
(b) The magnitude of (a + c) equals the magnitude of
( b + d),
(c) The magnitude of a can never be greater than the
sum of the magnitudes of b, c, and d,
(d) b + c must lie in the plane of a and d if a and d are
not collinear, and in the line of a and d, if they are
collinear ?
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