Rotational Motion Unit-03
1- The Shaft of a motor is rotating at constant angular velocity of 3000 RPM. The angle turned per
second is:
(a) 100 𝝅 𝒓𝒂𝒅/𝒔 (b) 200 𝝅 𝒓𝒂𝒅/𝒔 (c) 300 𝝅 𝒓𝒂𝒅/𝒔 (d) 400 𝝅 𝒓𝒂𝒅/𝒔
2- Two satellites are revolving around the Earth at a height Re and 3Re above the surface of the
Earth. The ratio of their velocities is:
𝟏 𝟏
(a) √𝟐 (b) (c) 2 (d) 𝟐
√𝟐
3- Global positioning system consists of how many satellites?
(a) 300 natural satellites (b) 150 artificial satellites
(c) 200 natural satellites (d) 200 artificial satellites
4- The expression for the orbital radius is:
𝟏 𝟏 𝟏 𝟏
𝟐 𝟑 𝟑 𝟑
𝒈𝑴𝑻𝟐 𝒈𝑴𝑻𝟐 𝑮𝑴𝑻𝟐 𝑮𝑴𝑻𝟐
(a) 𝒓 = (( 𝟐𝝅𝟐
)) (b) 𝒓 = (( 𝟐𝝅𝟐
)) (c) 𝒓 = (( 𝟒𝝅𝟐
)) (d) 𝒓 = (( 𝟐𝒓𝝅𝟐 ))
5- A car goes around a curve of radius r at a constant speed v. Then it goes around a curve of radius
2r at speed 2v. What is the centripetal force on the car as it goes around the second curve as
compared to the first?
(a) one-half as big (b) four times as big (c) one-fourth as big (d) twice as big
6- The time period of an Earth satellite revolving at a height of 35800 km is:
(a) 30 hours (b) 24 hours (c) 25 hours (d) 20 hours
7- A satellite is moving very close to a planet of density 𝝆. The time period of the satellite is:
𝟑𝝅 𝟑𝝅 𝟑𝝅 𝟑𝝅𝒓
(a) √𝝆𝒈 (b) √𝝆𝑮 (c) √𝟐𝝆𝒈 (d) √𝟐𝝆𝑮
8- A car moves with uniform circular motion. Which of the following best describes the angular
displacement, angular velocity and linear velocity of the car?
Angular Angular Linear
Displacement velocity velocity
A Constant Constant Constant
B Increase Constant Changes
C Constant Increase Changes
D Increase Increase Changes
9- In circular orbit of satellite of mass m, revolving around a planet of mass M in an orbit of radius r
and having the period of revolution T, we have:
𝑮𝑴 𝑮𝑴𝒎
(a) Orbital speed equals √ (b) Kinetic energy equals
𝒓 𝟐𝒓
𝟐 𝟑
(c) 𝑻 ∝ 𝒓 (d) All of these
10- A car is moving on a circular road of radius 225 m. At some instant, its speed is 30 m/s and is
increasing at a rate 3 m/s2. The magnitude of acceleration is:
(a) 3 m/s2 (b) 4 m/s2 (c) 5 m/s2 (d) 7 m/s2
11- Two particles of equal masses are revolving with the same linear speed on a circular track of radii
r1 and r2. The ratio of centripetal force acting on the particles will be:
𝒓 𝒓 𝟐 𝒓 𝒓 𝟐
(a) 𝒓𝟐 (b) (𝒓𝟐) (c) √𝒓𝟐 (d) (𝒓𝟏)
𝟏 𝟏 𝟏 𝟐
12- A geostationary satellite is launched such that it moves from:
(a) North to South on polar plane (b) South to North on polar plane
(c) East to West in the equatorial plane (d) West to East in the equatorial plane
13- A wheel having diameter of 3 m starts from rest and accelerates uniformly to an angular velocity
of 210 RPM in 5 seconds. Angular acceleration of the wheel is:
(a) 4.4 rad/s (b) 2.2 rad/s (c) 3.3 rad/s (d) 1.1 rad/s
14- A satellite is orbiting around the Earth with a period T. If the Earth shrinks suddenly to half of its
radius without changing in mass, the period of revolution of the satellite will be:
𝑻 𝑻 𝑻
(a) (b) (c) (d) 𝑻
√𝟐 𝟐 𝟐√𝟐
15- A disc is rotating about an axis through its centre and perpendicular to its plane. A point P on the
disc is twice as far from the axis as point Q. At a given instant, what is the value of the linear
𝒕𝒉𝒆 𝒍𝒊𝒏𝒆𝒂𝒓 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒐𝒇 𝑷
velocity of 𝒕𝒉𝒆 𝒍𝒊𝒏𝒆𝒂𝒓 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒐𝒇 𝑸 ?
(a) 4 (b) 2 (c) 1/2 (d) ¼
16- A mass of 2 kg is tied to one end of a string 5 m long and is rotated at constant speed of 30 m/s in a
vertical circle. The ratio of the tensions at the top and the bottom is ( g= 1-0 m/s2 )
(a) 1:2 (b) 16:17 (c) 13:15 (d) 17:19
17- A turn table, initially at rest, is set in motion with a uniform angular acceleration ∝. Its angular
velocity in rad/s at the end of one complete revolution is:
(a) √𝝅 ∝ (b) 3√𝝅 ∝ (c) 2√𝝅 ∝ (d) 𝟒√𝝅 ∝
18- Assume that the time period of a satellite close to the surface of the Earth is 80 minutes. What is
the time period of another Earth satellite in an orbit of radius equal to four times the Earth’s
radius?
(a) 640 minutes (b) 680 minutes (c) 660 minutes (d) 720 minutes
19- A roller coaster car is on the track that forms a circular loop in the vertical plane. If the car is to
just maintain contact with track at the top of the loop, what is the minimum value for its
centripetal acceleration at this point?
(a) g upward (b) g downward (c) 0.5g downward (d) 2g upward
20- An automobile engine develops 105 W when rotating at a speed of 1800 rev/min. The torque
delivered by the engine?
𝟏𝟎𝟐 𝟏𝟎𝟔 𝟏𝟎𝟒 𝟏𝟎𝟖
(a) 𝟔𝝅 𝑵𝒎 (b) 𝟔𝝅 𝑵𝒎 (c) 𝟔𝝅 𝑵𝒎 (d) 𝟔𝝅 𝑵𝒎
21- Which of the following quantities remain constant in a planetary motion (consider elliptical orbits)
as seen from the Sun?
(a) Speed (b) K.E (c) Angular speed (d) Angular momentum
22- If a satellite moves above Earth’s atmosphere in a circular orbit with constant speed, then:
(a) its acceleration and velocity are always in the same direction
(b) the net force on it is zero
(c) it will fall back to Earth when its fuel is used up
(d) its acceleration is toward the Earth
23- If a certain car, going with speed v1, rounds a level curve with a radius R1, it is just on the verge of
skidding. If its speed is now doubled, the radius of the tightest curve on the same road that it can
round without skidding is:
(a) 2R1 (b) 4R1 (c) R1/2 (d) R1/4
24- One end of a 1.0-m long string is fixed, the other end is attached to a 2.0-kg stone. The stone
swings in a vertical circle, passing the bottom point at 4.0m/s. The tension force of the string at
this point is about:
(a) 0 (b) 12N (c) 20N (d) 52N
25- An object moves in a circle. If the mass is tripled, the speed halved, and the radius unchanged,
then the magnitude of the centripetal force must be multiplied by a factor of:
(a) 3/2 (b) 3/4 (c) 9/4 (d) 6
26- A 0.2-kg stone is attached to a string and swung in a circle of radius 0.6m on a horizontal and
frictionless surface. If the stone makes 150 revolutions per minute, the tension force of the string
on the stone is:
(a) 0.03N (b) 0.2N (c) 0.9N (d) 30N
27- An object of mass m and another object of mass 2m are each forced to move along a circle of
radius 1.0m at a constant speed of 1.0m/s. The magnitudes of their accelerations are:
(a) equal
(b) in the ratio of √2:1
(c) in the ratio of 2 : 1
(d) in the ratio of 4 : 1
