1. A force P of 50 N and another force Q of unknown magnitude act at 90° to each other. They are balanced by a force of 130 N. The magnitude of Q is
a) 60 N
b) 80 N
c) 100 N
d) 120 N
Ans: d
2. If the resultant of two forces has the same magnitude as either of the force, then the angle between the two forces is
a) 30°
b) 45°
c) 60°
d) 120°
Ans: d
3. A rod AB carries three loads of 30 N, 70 N and 100 N at distances of 20 mm, 90 mm and 150 mm respectively from A. Neglecting the weight of the rod, the point at which the rod will balance is
a) 109.5 mm from A
b) 119.5 mm from A
c) 125.5 mm from A
d) 132.5 mm from A
Ans: a
4. The angles between two forces to make their resultant a minimum and a maximum respectively are
a) 0° and 90°
b) 180° and 90°
c) 90° and 180°
d) 180° and 0°
Ans: d
5. When two forces, each equal to P, act at 90° to each other, then the resultant will be
a) P
b) PV2
c) P/V2
d) 2P
Ans: b
6. The resultant of two forces P and Q is R. If Q is doubled, the new resultant is perpendicular to P. Then,
a) P = R
b) Q = R
c) P = Q
d) None of the above is correct
Ans: b
7. A cube on a smooth horizontal surface
a) cannot be in stable equilibrium
b) cannot be in neutral equilibrium
c) cannot be in unstable equilibrium
d) can be in any of these states
Ans: d
8. The following is in unstable equilibrium
a) a uniform solid cone resting on a generator on a smooth horizontal plane
b) a uniform solid cone resting on its base on a horizontal plane
c) a solid cube resting on one edge
d) a satellite encircling the earth
Ans: c
9. A block in the shape of a parallelopiped of sides lm x 2m x 3m lies on the surface. Which of the faces gives maximum stable block ?
a) 1 m x 2 m
b) 2 m x 3 m
c) 1 m x 3m
d) equally stable on all faces
Ans: b
10. A uniform pyramid and a uniform prism of same height lie with their base on the surface. Which is more stable ?
a) pyramid
b) prism
c) both equally stable
d) none of the above
Ans: a
11. Minimum potential energy of a system will be in the position of
a) stable equilibrium
b) unstable equilibrium
c) neutral equilibrium
d) all of the above
Ans: a
12. A rigid body is in a stable equilibrium if the application of any force
a) can raise the CG of the body but can not lower it
b) tends to lower the CG of the body
c) neither raises nor lowers the CG of the body
d) none of above
Ans: a
13. Which of the following represents the state of neutral equilibrium ?
a) a cube resting on one edge
b) a smooth cylinder lying on a curved surface
c) a smooth cylinder lying on a convex surface
d) none of the above
Ans: d
14. Two circular discs of same weight and thickness are made from metals having different densities. Which disc will have the larger rotational inertia about its central axis ?
a) disc with larger density
b) disc with smaller density
c) both discs will have same rotational inertia
d) none of the above
Ans: b
15. The total kinetic energy of a hoop of mass 2 kg and radius 4 m sliding with linear velocity 8 m/sec and angular velocity 5 radian/sec is
a) 64 J
b) 400 J
c) 464 J
d) 89 J
Ans: c
16. A symmetrical body is rotating about its axis of symmetry, its moment of inertia about the axis of rotation being 2 kg m2 and its rate of rotation 2 revolutions/see. The angular momentum of the body in kg-m2/sec is
a) 4
b) 6 7i
c) 8TC
d) 8
Ans: c
17. The angular speed of a car while taking a circular turn of radius 100m at 36 km/hour, is
a) 0.1 radian/sec
b) 1 radian/sec
c) 100 radian/sec
d) 1000 radian/sec
Ans: a
18. The torque produced by a force depends on
i) the magnitude of the force
ii) the direction of the force
iii) the’point of application of the force relative to origin
The correct answer is
a) only (i)
b) both (i) and (ii)
c) both (i) and (iii)
d) all (i), (ii) and (iii)
Ans: d
19. The ratio of the speed of a rolling cylinder to the speed of sliding cylinder is
a) less than 1
b) equal to 1
c) between 1 and 2
d) greater than 2
Ans: a
20. A sphere and a cylinder having the same mass and radii start from rest and roll down the same inclined plane. Which body gets to the bottom first ?
a) sphere with greater rotational energy at bottom than cylinder
b) sphere with lesser rotational energy at bottom than cylinder
c) cylinder with greater rotational energy at bottom than sphere
d) both reach the bottom simultaneously with equal rotational energy at bottom
Ans: b
21. A hoop of radius 3 m weighs 100 kg. It rolls along a horizontal floor so that at its centre of mass has a speed of 200 mm/sec, . The work required to stop the hoop is
a) 2 J
b) 4 J
c) 6 J
d) 8 J
Ans: b
22. A solid cylinder of mass M and radius R rolls down an inclined plane without slipping. The acceleration of centre of mass of rolling cylinder is
a) (1/3) g sinB
b) (2/3) g cos 9
c) (2/3) g sin 0
d) g sin 9
where ‘g’ is acceleration due to gravity and 0 is inclination of plane with horizontal.
Ans: c
23. A solid sphere of mass M and radius R rolls down a plane inclined at 0 with the horizontal. The acceleration of sphere is
a) (1/3) g sin0
b) (2/5) g sin 0
c) (3/7) g sin 0
d) (5/7) g sin0
where g is acceleration due to gravity
Ans: d
24. A cylinder will slip on an inclined plane of inclination 0 if the coefficient of static friction between plane and cylinder is
a) less than (1/3) tan 0
b) less than (2/3) tan 0
c) less than (1/3) sin 6
d) less than (2/3) sin 6
Ans: a
25. Rate of change of angular momentum is equal to
a) force
b) torque
c) linear momentum
d) impulse
Ans: b