26. If the angular distance, 0 = 2t3 – 3t2, the angular acceleration at t = 1 sec. is
a) 1 rad/sec2
b) 4 rad/sec2
c) 6 rad/sec2
d) 12 rad/sec2
Ans: c
27. A circular disc rotates at n rpm. The angular velocity of a circular ring of same mass and radius as the disc and to have the same angular momentum is
a) n rpm
b) n/2 rpm
c) n/4 rpm
d) 2n rpm
Ans: b
28. A particle moves in a straight line and its position is defined by the equation x = 6 t2 – t3 where t is expressed in seconds and x in metres. The maximum velocity during the motion is
a) 6 m/sec
b) 12 m/sec
c) 24 m/sec
d) 48 m/sec
Ans: b
29. A flywheel of moment of inertia 20 kg-m” is acted upon by a tangential force of 5 N at 2 m from its axis, for 3 seconds. The increase in angular velocity in radian persecond is
a) 1/2
b) 3/2 ‘
c) 2
d) 3
Ans: b
30. A disc of mass 4 kg, radius 0.5m and moment of inertia 3 kg-m2 rolls on a horizontal surface so that its centre moves with speed 5 m/see. Kinetic energy of the disc is
a) 50 J
b) 150 J
c) 200 J
d) 400 J
Ans: c
31. When a circular wheel rolls on a straight track, then the shape of body centrode and space centrode respectively are
a) straight line and parabola
b) straight line and circle
c) circle and straight line
d) circle and parabola
Ans: c
32. Select the correct statement
a) The body centrode rolls on the space centrode.
b) The space centrode rolls on the body centrode.
c) Both body and space centrodes may role on each other.
d) The body centrode never touches space centrode.
Ans: a
33. At the instantaneous centre, the velocity of the moving lamina at any instant is
a) zero
b) maximum
c) minimum
d) varying
Ans: a
34. Instantaneous centre is at infinity when the angular velocity is
a) constant
b) zero
c) maximum
d) minimum
Ans: b
35. A 2 m long ladder rests against a wall and makes an angle of 30° with the horizontal floor. Where will be the instantaneous centre of rotation when the ladder starts slipping ?
i) 1.0 in from the wall
ii) 1.732 m from the wall
iii) 1.0 m above the floor
iv) 1.732 m above the floor
The correct answer is
a) (i) and (iii)
b) (i) and (iv)
c) (ii) and (iii)
d) (ii) and (iv)
Ans: d
36. For a given velocity of a projectile, the range is maximum when the angle of projection is
a) 30°
b) 45°
c) 90°
d) 0°
Ans: b
37. The angle of projection at which the horizontal range and maximum height of a projectile are equal to
a) 36°
b) 45°
c) 56°
d) 76°
Ans: d
38. The maximum value of the horizontal range for a projectile projected with a velocity of 98 m/sec is
a) 98 m
b) 490 m
c) 980 m
d) 1960m
Ans: c
39. A stone is thrown vertically upwards with a vertical velocity of 49 m/sec. It returns to the ground in
a) 5 sec
b) 8 sec
c) 10 sec
d) 20 sec
Ans: c
40. A projectile has maximum range of 40 m on a horizontal plane. If angle of projection is a and the time of flight is 1 second, then sin a must be about
a) 1/4
b) 1/3
c) 1/2
d) 1/5
Assume g = 10 m/sec2
Ans: a
41. If the direction of projection bisects the angle between the vertical and the inclined plane, then the range of projectile on the inclined plane is
a) zero
b) maximum
c) minimum
d) unpredictable
Ans: b
42. If a projectile is fired with an initial velocity of 10 m/sec at an angle of 60° to the horizontal, its horizontal and vertical velocity at the highest point of trajectory are
a) 0 and 5 m/sec
b) 5 m/sec and 0
c) 5 V3 m/sec and 0
d) 5 and 5V3 m/sec
Ans: b
43. The angle of projection at which the horizontal range and maximum height of a projectile are equal to
a) 45°
b) tan-1 (2)
c) tan-‘ (4)
d) tan”1 (1/4)
Ans: c
44. A stone is thrown up a slope of inclination 60° to the horizontal. At what angle to the slope must the stone be thrown so as to land as far as possible from the point of projection ?
a) 15°
b) 30°
c) 45°
d) 75°
Ans: a
45. In a simple harmonic motion, the position of equilibrium is always
a) stable
b) unstable
c) neutral
d) none of the above
Ans: a
46. If A is the amplitude of particle executing simple harmonic motion, then the total energy E of the particle is
a) proportional to A
b) proportional to A2
c) proportional to 1/A2
d) independent of A
Ans: b
47. The time period of a simple pendulum depends on
i) mass of suspended particle
ii) length of the pendulum
iii) acceleration due to gravity
The correct answer is
a) only (i)
b) both (ii) and (iii)
c) both (i) and (iii)
d) all are correct
Ans: b
48. A particle of mass 2 kg executes simple harmonic motion of frequency 6/71 Hz and amplitude 0.25 m. Its maximum kinetic energy is
a) 4.5 J
b) 9.0 J
c) 12.0 J
d) 18.0 J
Ans: b
49. The maximum displacement of a particle executing S.H.M. corresponds to
a) zero potential energy and maximum kinetic energy
b) zero kinetic energy and maximum potential energy
c) maximum kinetic energy and maxi-mum potential energy
d) minimum kinetic energy and minimum potential energy
Ans: b
50. It is observed that in a certain sinusoidal oscillation, the amplitude is linearly dependent on the frequency f. If the maximum velocity during the oscillation is V, then V must be proportional to
a) f
b) 1/f
c) 1/f2
d) f2
Ans: d