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 hori¬zontal.
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
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
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 hori¬zontal.
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
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
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