1. Aparticle is moving on a circular path.
2
sin 94
The angle turned by radius vector is (b) cos
R R
e -(1 -e ), where is in radian and
tis in second. The angular acceleration (c) COs 9; sin 9 j
R R
at t= 0 is
1
(a) rad s2 1 (d) i+;
3
(b) rad s-2
R R
3. A particle moves on a circular path of
(c) 10 rad s-2 (d) -- rad s-2 radius 0.2 m with an angular acceleration
6
0.25 rad s-2. The particle starts from
2. For aparticle in auniform circular motion, rest, find the time at which the
the acceleration a at a point P(R, 0) on the magnitude of radial acceleration and
circle of radius R is (here, 0 is measured
from the -axis)
the magnitude of tangential acceleration
are same.
(a) (a) 1 s (b) 2 s
cos 0i+ sin j
R R (c) 3 s (d) 4 s
ANSWERS
de /3
|1. (b) :8= (1-et3), so, ) = dt 3
a=
R
towards centre of circle
do [centripetal acceleration)
- e / 3
or
dt
1 -2
a= (-cosei-sine,)
R
At t= 0, a=-rad s
9
|2. (c): For a particle in a uniform circular R -cose i-sn®j
R
motion 3. (b) : a; =a,
Or ra = r0² or a = 0² or 0.25 = 2
PR, 0) () = V25x10 -0.5 rad s1
() =at or 0.5 = 0.25t
5x10 10
t=
25x10-2-==2s
5
1. In the uniform circular motion, 5. Three identicai particle as shown in igure
(a) acceleration andvelocity both remain tied with string and speed of outermost
constant particle is v then ratio T,: T,: T, will be
(b) acceleration and speed both remain (where I, is tension in outside string)
constant
(c) acceleration and velocity both keep m
on changing
(d) acceleration and speed both change
(a) 3: 5:7 (b) 3:5:6
2. If aparticle moves in a circle, describing (c) 3:4:5 (d) 7:5:3
equal angles in equal intervals, the velocity
vector 6. A car passes alorng a curved path of a
(a) remains constant road according to figure moving with
(b) changes in magnitude speed of 72 km h, radius of curve is 10
(c) changes in direction m. If mass of the car is 500 kg, reaction
(d) changes both in magnitude and force on car at lowest point of curved
direction part will be
3. When a body moves with a constant
speed along acircle P
(a) no work is done on it (a) 25 kN (b) 50 kN
(b) no acceleration is produced in the (c) 75 kN (d) None of these
body
(c) no force acts on the body
7. A motorcycle is going on an over bridge of
radius R. The driver maintainsa constant
(d) its velocity remains constant
speed. As the motorcycleis ascending on
4. A mass is supported on a frictionless the over bridge, the normal force on it
horizontal surface. It is attached to (a) increases
string and rotates about aixed centre (b) decreases
at an angular velocity o. lf the length (c) remains same
of the string and angular velocity are (d) tluctuates
doubled, the tension in the string which 8. A car is travelling with linear velocity r
was initially T, is now on acircular road of radius r. If the speed
(a) To (b) T/2 is increasing at the rate of am s, then
(c) 4To (d) 8T, the resultant acceleration will be
(a) 3.7 m s² (b) 2.7 ms2
(a) (b) (c) 1.8 m s2 (d) 2.0 ms
10. A particle describes a horizontal circle
(c) (d) in a conical funnel whose inner surface
is smooth with speed of 0.5 m s. What
9. A car is moving with speed of 30 m s is the height of the plane of circle from
on a circular path of radius 500 m. If it vertex of the funnel?
increases its speed at the rate of 2 ms-? (a) 0.25 cm (b) 2 cm
the resultant acceleration will be
(c) 4 cm (d) 2.5 cm
ANSWERS
1. (c) 2. (c)
3. (a)
4. (d) :T, =mar
and T = m(2o)(2r) = 8T, a=
5. (b): T =mo(3)
I,- T, - mo{2/) 9. (b) :v=30 ms-l, r =500 m,
T,- ma(51) du
=2 m s2
T, - T, - mal dt
’ T,= mo(6/) 30
I:T, :T, =3:5:6 |2+| - 2.7 ms-2
500
72x 1000 1
my
6. fa) : a, = X
10. (d) :N sin 0 =
3600 10
= 40 m s2 and N cos = ng
F, = ma, = (500 x 40) = 20000 N= 20 kN
F, mg= (500 x 10) =5000 N =5 kN tan =
Reaction force,F= 20 kN +5 &N= 25 kN rg mg
h 2
or
7. (b): mg (at highest point)
dv =A m s-2 h= =2.5 cm
8. (b) : a, = 8 10
dt
