A particle of mass 21g is attached to a string of length 70cm
A particle of mass 21g is attached to a string of length 70cm VI 04
MOTION ALONG A HORIZONTAL CIRCL€
AND MOTION OF VEHICLE ALONG
CIRCULAR TRACKS
24. A particle of mass 21 g attached to a string of
70 cm length is whirled in a horizontal circle. If
the of revolution is 2 s, find the tension in
[Ans. 14509 dyne]
the string.
A ball of mass 0-1 kg is by a string 30
cm long. Keeping the string always taut, the ball
describes a horizontal circle Of radius
cm. Calculate the angular SB•ed Of the ball.
(Ans. 6•14 rad./sl
26. A car of mass ISOOkg is moving with a speed Of
rns-l on a circular path of radius 20 m on a
level road What should the frictional force to
avoid slipping Of car. Calculate the coefficient of
[Ans. 1-172 N ; 0-81
27. What is angular velocity in rad s-l Of the hour,
minute and second hand of a clock ?
3. What is the greatest speed at which a car having a
track width of I S m can turn in a circular path of
24-5 m without overturning ? Assume that
centre of gravity of the car is 049 m above the
grcnand. Take g 98 mis2_
[Ans. 19•2 misl
29. of a massless svmng Of constant Im Nim
natural length 0-5 m is fixed and the other end
is connected to a particle of mass kg lying on a
frictionless horizontal table. ne spring remains
horizontal. If the mass is made to rotate at an
uvular vel•xity of 2 rd's, find the elongation of
smng.
[Ans. I cml
A of mass kg is whirled in a circle with a
of 2 m s"' using m length of a string,
which can withstand a tension of 15 N. Neglecting
the force of gravity On the body. predict whether
or tix string will break. Give reasons for ymar
(Ans. The string will not break Centrifugal
force is 4 N, which less than IS NI
31. The blades of an acroplanc pros*ller are 2 m long
rate Of rpm, Calculate (i) the
frequency Erriod of rotation (iii) the angular
vehxity the unear vel'Rity of a B)int 0-5 m
up of blade ,
S ; 3143 ; 47-15 m
32. maxunum SCRed at which a Car can turn
a curve or 30 m radius on a level road if the
of friction txtween the tyres and the
[Ans. 11 m s-ll
4
33. A bend in a level road has a radius 01
the maximum speed which a car
turning t:
may have Without skidding. Coefficient of
between tyres and road is 018.
28
AND BANKING OF R
34. An aeroplane travelling at a Of
tilts at an angle of as it makes a Safe
is the radius Of tlr curve ? [Ans. 3•41
35. A curve in a road forms an arc of radius "m
the road is 196 m wide and outer edge i'
higher than the inner edge, calculate the
which it is banked.
[Ans. 20
36. For traffic moving at 60 km/h, if the radius
curve is (VI km. what is the correct angle
banking of the road ? Given g 10
(Ans.
37. A cyclist goes round a circular track of 440
length in 20 seconds. Find the angle that his
makes with the vertical.
[Ans.3s•
38. A cyclist speeding at IS km/h on a level road
a sharp circular turn Of radius 3 m without
his speed. Will the cyclist slip while taku
turn. if coefficient Of friction between the tyresQ
road is 0-1 ?
I Ans
39. An electric bulb suspended from the
railway train by a flexible wire shifts
angle of 190 48'. when the train goes
round a curved path of 200 m radius. find
Slk•ed of the train.
[Ans. 26•56
A 200 kg car has to go over a turn Whose
750 m and the angle of slope is The
of friction between the car wheels and
0-5. What should be the maximum speed Of
car so that it may go Over the turn Wi
slipping ? Take g = 9 •8 mjs2, (Ans. 672
41. A rnotor cyclist goes round a circular
of diameter 320 m at 144 krn.m. How far fm
vertical must he lean inwards to keep his balang
Take g = 10m
42. The radius of curvature of a railway trackat•
where the train is moving at a speed Of 72 kni
is 625 m, Ille distance between the rails is
Find the angle and the elevation Of the outa
so that there may be no side pressure on the
Take g 9-8 ms-2.
[Ans. 3-74• ;
MOTION A VERTICAL ciRC
43. ne railway bridge over a canal is in the
an arc of a circle Of radius 20 m. What is
minimum speed with which a car can crcss