23277.A body is allowed to slide on a frictionless track from rest under–gravity. The track ends in a circular loop of diameter D. What should be the minimum height of the body in terms of D, so that it may successfully complete the loop?
$\dfrac{4}{5}$ D
$\dfrac{5}{4}$ D
D
2D
23278.An electron revolve around the nucleolus the radius of the circular orbit is r to double the kinetic energy of electron its orbit radius of
$\sqrt{2}$r
–$\sqrt{2}$r
$\sqrt{3}$r
–$\sqrt{3}$r
23279.A body is traveling in a circle at constant speed. It
has constant velocity.
has no acceleration
has an inward acceleration
has an outward radial acceleration
23280.A body of mass 100 gram, tied at the end of a string of length 3 m rotates in a vertical circle and is just able to complete the circle. If the tension in the string at its lowest point is 3.7 N, then its angular velocity will be ______ (g = 10 m/s2)
4 rad/s
3 rad/s
2 rad/s
1 rad/s
23281.A particle P is moving in a circle of radius ‘a’ with uniform speed v. C is the centre of the circle and AP is diameter. The angular velocity of P about A and C are in the ratio
1 : 1
1 : 2
2 : 1
4 : 1
23282.A body of mass 500 gram is rotating in a vertical circle of radius 1 m. What is the difference in its kinetic energies at the top and the bottom of the circle?
4.9 J
19.8 J
2.8 J
9.8 J
23283.The maximum velocity with which a driver must drive his car on a flat curved road of radius of curvature 150 m and coefficient of friction 0.6, to avoid the skidding of his car is (take g = 10 m/s2)
60 m/s
50 m/s
40 m/s
30 m/s
23284.The driver of a car traveling at velocity v suddenly sees a broad wall in front of him at a distance a. He should
break sharply
turn sharply
both a and b
none of the above
23285.A body of mass m is suspended from a string of length l. What is the minimum horizontal velocity that should be given to the body in its lowest position so that it may complete full revolution in the vertical plane with the point of suspension at the center of circle?
$\sqrt{2gl}$
$\sqrt{3gl}$
$\sqrt{4gl}$
$\sqrt{5gl}$
23286.A cyclist is moving in a circular track of radius 80 m, with a velocity of 36 km/hour. In order to keep his balance, he has to lean inwards from the vertical through an angle q. If g = 10 m/s2, then q is given by
tan–1 (2)
tan–1 (4)
tan–1 $\dfrac{1}{4}$
tan–1 $\dfrac{1}{8}$
23287.A body of mass m performing UCM with frequency n along the circumference of circle having radius r, force is given by
4$π$nm2
4$π$2n2m
$π$2n2mr
$\dfrac{1}{2}$πnm2
23288.A bucket containing water is tied to one end of a rope of length 2.5 m and rotated about the other end in a vertical circle. What should be the minimum velocity of the bucket at the highest point, so that the water in the bucket will not spill? (g = 10 m/s2)
2.5 m/s
4 m/s
5 m/s
7 m/s
23289.A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with a constant speed. What should be the minimum speed so that the water from the bucket does not spill when the bucket is at the highest position?
4 m/sec.
6.25 m/sec.
16 m/sec.
None of these
23290.A can filled with water is revolved in a vertical circle of radius 4 metre and the water does not fall down. The time period of revolution will be
1 sec
10 sec
8 sec
4 sec
23291.A car is moving in horizontal circular track of radius 10 m, with a constant speed of 36 km/hour. A simple pendulum is suspended from the roof of the car. If the length of the simple pendulum is 1 m, what is the angle made by the string with the track?
30°
45°
60°
90°
23292.A car is moving in a circular track of radius 10 metre with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of 1 metre long. The angle made by the rod with the track is
zero
30°
45°
60°
23293.A car is moving with a speed of 30 m/s on a circular path of radius 500 m. Its speed is increasing at the rate of 2 m/s2. The acceleration of the car is
9.8 m/s2
1.8 m/2
2 m/s2
2.7 m/s2
23294.In the case of uniform circular motion, which one of the following physical quantities does not remain constant?
mass
speed
linear momentum
kinetic energy
23295.A van is moving with speed of 108 km/hr. on level road where coefficient of friction between tires and road 0.5. For the safe driving of van the minimum radius of curvature of the road will be (g = 10 m/s2)
80 m
40 m
180 m
20 m
23296.A pulley one metre in diameter rotating at 600 r.p.m. is brought to rest in 80 sec. by a constant force of friction on its shaft. How many revolutions does it makes before coming to rest?
200
300
400
500