Circular Motion (Including clocks) – I
TSD is one of the most important topics for CAT and other management entrance exams, questions from
which have appeared consistently in all these exams.
Key concepts discussed:
•
If two persons start running simultaneously on a on circular track of length L in same direction at
speeds u and v, then
o
o
o
•
L
The time after which they meet for the first time anywhere on the track is u − v ;
L L 
The time after which they meet for the first time at the starting point on the track is LCM  ,  ;
u v 
The number of distinct points on the track at which they will meet is |x – y|, where x : y is equal
to the ratio of u to v in the simplest form i.e. the ratio of the speeds of the runners.
If two persons start running simultaneously on a on circular track of length L in opposite directions
at speeds u and v, then
o
o
o
L
The time after which they meet for the first time anywhere on the track is u + v ;
The time after which they meet for the first time at the starting point on the track is
L L 
LCM  ,  ;
u v 
The number of distinct points on the track at which they will meet is (x + y), where x : y is equal
to the ratio of u to v in the simplest form i.e. the ratio of speeds of the runners.
Highlight: This session deals with questions which are based on basic concept of Circular Motion. Questions
in the session are of easy to moderate difficulty level.
Session
TSD & Work
The questions discussed in the session are given below along with their source.
DIRECTIONS for Question 1: The question is followed by two statements, I and II. Mark the answer
(a) if the question can be answered with the help of one statement alone.
(b) if the question can be answered with the help of any one statement independently.
(c) if the question can be answered with the help of both statements together.
(d) if the question cannot be answered even with the help of both statements together.
Q1.
After what time will the two persons Tez and Gati meet while moving around the circular track? Both
of them start at the same point and at the same time.
I. Tez moves at a constant speed of 5 m/s, while Gati starts at a speed of 2 m/s and increases his
speed by 0.5 m/s at the end of every second thereafter.
II. Gati can complete one entire lap in exactly 10 s.
(CAT 1997)
Q2.
A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute)
πr
πr
πr
during next one minute,
during next 2 minutes,
during
8
2
4
next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the
previous round?
(a) 4
(b) 8
(c) 16
(d) 32
(CAT 2004)
is πr during the first 30 seconds,
Q3.
A jogging park has two identical circular tracks touching each other, and a rectangular track enclosing
the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start
jogging simultaneously form the point where one of the circular tracks touches the smaller side of
the rectangular track. A jogs along the rectangular track, while B jogs along the two circular tracks
in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the
same time to return to their starting point?
(a) 3.88%
(b) 4.22%
(c) 4.44%
(d) 4.72%
(CAT 2005)
Q4.
A and B starts together from the same point on a circular track and walk in the same direction till
they both again arrive together at the starting point. A completes one complete round in 224 s and
B in 364 s. How many times will A have passed B?
(a) 4
(b) 5
(c) 6
(d) 7
(e) 8
(CL material)
Q5.
Ram and Suraj start running from point A on a circular track of 1,200 m. Ram runs at a speed of 12
km/hr and Suraj at a speed of 8 km/hr. They start running in opposite directions at the same time.
When each of them reaches at point A for the first time, they reverse their directions along the track.
In how much time after starting will they meet for the second time?
(a) 7.2 min
(b) 7.8 min
(c) 10.8 min
(d) 11.2 min
(e) 9.4 min
(CL material)
TSD & Work
Session