CHAPTER 5 ROTATIONAL AND CIRCULAR MOTION

 

5.1      Select the best option of the following question.

1.      85.95° degree in term of radian is
(a) 1/2 radian	(b) 1 radian
(c) 1+1/2 radian	(d) 2 radians
2.      What is the circumference of a circle, having radius of 50 cm?
(a) 3.12 m	(b) 3.14 m
(c) 3.16 m	(d) 3.18 m
3.      What is the angular velocity of a particle when its frequency is 50 Hz?
(a) 312 rad s-1	(b) 313 rad s-1
(c) 314 rad s-1	(d) 315 rad s-1
4.      The direction of angular velocity is along;
(a) Tangent the circular path	(b) Axis of rotation
(c) Inward the radius	(d) Outward the radius Angular
5.      Angular speed for annual rotation of earth in radian per day.
(a) π/2 radian/day	(b) π radian/day
(c) 2 π radian/day	(d) 365 radian/day
6.      A body moves with constant angular velocity on a circle. Magnitude of angular Acceleration is
(a) rω2	(b) Constant
(c) Zero	(d) rω
7.      Banking angle does not depend upon
(a) Mass	(b) Speed
(c) Radius	(d) Gravitational acceleration
8.      What will be happened? When the height of an orbit of a satellite from surface of earth is increased,
(a) Speed increases	(b) Angular velocity increases
(c) Time period increases	(d) Gravitational acceleration increases
9.      What should be the ratio of translational and rotational kinetic energies of a solid sphere
(a) 1/2	(b) 2/3
(c) 5/2	(d)  2/5
10.  Angular momentum in term of moment of inertia is
(a) Iω	(b) Iω2
(c) I2ω	(d) I/ω2
11.  Which one of the following rolling body has 50% translational K.E and 50% rotational K.E
(a) Disc	(b) Ring
(c) Rod	(d) Sphere
12.  A solid cylinder of mass 20 kg rotates about its axis with angular velocity of 10 m/s radius 0.2m. The moment of inertia of the cylinder is
(a) 0.2 kg m2	(b) 0.4 kg m2
(c) 0.6 kg m2	(d) 0.8 kg m2
13.  The condition of weightless is (N=Normal Reaction and Wis weight)
(a) N > W	(b) N < W
(c) N = W	(d) N = 0
14.  A sphere is rolling without slipping on a horizontal plane. The ratio or Rotational kinetic energy and translational kinetic energy is
(a) 2:3	(b) 2:5
(c) 2:7	(d) 2:9
15.  The frequency of artificial gravity is
(a) 2π√g/R	(b) 2π√R/g
(c) 1/2π(√R/g)	(d) 1/2π(√g/R)
16.  A particle of mass 100 g starts its motion from rest along a circular path Radius 10 cm. If its velocity becomes 10m/ sec then its centripetal force is;
(a) 0.1 N	(b) 1 N
(c) 10 N	(d) 100 N
17.  Which one of the following is conserved when the torque acting on a system is zero
(a) K. E	(b) Angular momentum
(c) Rotational K. E	(d) Linear momentum
18.  Orbital velocity of earth’s satellite near the surface is 7 km/s. When the radius of the orbit is 4 times than that of earth’s radius then orbital velocity in that Orbit is
(a) 3.5 kms-1	(b) 7 kms-1
(c) 7√2 kms-1	(d) 14 kms-1
19.  When a parachutist is moving downward with uniform motion then its weight is
(a) Decreasing	(b) Increasing
(c) Remain same	(d) Zero
20.  An object of mass 1.5 Kg, suspended by a string having tension T= 5 N in a Lift, when the lift is moving upward with acceleration a = 2 ms-2 then its apparent weight is
(a) 8 N	(b) 5 N
(c) 2N	(d) 1.5 N

 

Answers

1. (c) 1+1/2 radian
2. (b) 3.14 m
3. (c) 314 rad s^-1
4. (b) Axis of rotation
5. (c) 2π radian/day
6. (c) Zero
7. (a) Mass
8. (c) Time period increases
9. (c) 5/2
10. (a) Iω
11. (d) Sphere
12. (b) 0.4 kg m²
13. (d) N = 0
14. (b) 2:5
15. (d) 1/2π √(g/R)
16. (d) 100 N
17. (b) Angular momentum
18. (a) 3.5 kms^-1
19. (a) Decreasing
20. (c) 2N

5.2      Short question

5.      How can you calculate the angular velocity of earth about its axis in rad/s?

17.      What is the frequency of oscillations of a simple pendulum inside an artificial Satellite?

5.3      Numerical problems

1. The earth completes one rotation about its axis in 24 hours. Calculate (a) the Angular speed of the earth (b) tangential speed of body at the equator.

4. A body of mass ‘m’ connected with a string of length ‘l’, is whirled in a horizontal circle. Find the centripetal force (a) when the length of the string is doubled (b) when the tangential velocity of the body is doubled.

7. The gravitational force on a satellite exerted by earth on its surface is ‘F’. What will be the gravitational on the satellite, when it is at a height of R/50. Where ‘R’ is the radius of the earth.

12. With what speed does a space station rotate in order to produce at its outer rim an artificial gravity equal to 9.8 ms^-2? The radius of the space station is 85 m. Also calculate its period of rotation.