Whenever a body is released from height, it travels vertically downward towards the surface of earth. This is due to the force of gravitational attraction exterted on body by the earth. The acceleration produced by this force is called acceleration due to gravity and is denoted by ‘g’. Value of ‘g’ on the surface of earth is taken to the 9.8 m/s2 and it is same for all the bodies. It means all bodies (whether an iron ball or a piece of paper), when dropped (u=0) from same height should fall with same rapidity and should take same time to reach the earth. Our daily observation is contrary to this concept. We find that iron ball falls more rapidlly than piece of paper. This is due to the presence of air which offers different resistance to them. In the absence of air both would have taken same time to reach the surface of earth.
A particle of mass m is attached to a light and inextensible string. The other end of the string is fixed at O and the particle moves in a vertical circle of radius r equal to the length of the string as shown in the figure.
Forces Acting on the Particle
Consider the particle when it is at the point P and the string makes an angle θ with vertical. Forces acting on the particle are:
T = tension in the string along its length, and
mg = weight of the particle vertically downward.
Hence, net radial force on the particle is FR = T - mg cos θ
=> T - mg cos θ = mv2/R
=> T = mv2/R + mg cos θ
Since speed of the particle decreases with height, hence tension is maximum at the bottom, where cos θ = 1 (as θ = 0).
=> Tmax = mv2/R + mg; Tmin = mv'2/R - mg (at the top)
Here, v' = speed of the particle at the top.
NEET - Physics Circular Motion Practice Q & A Page: 3
23317.A car is moving on a circular path and takes a turn. If R1 and R2 are the reactions on the inner and outer wheels respectively, then
R1 = R2
R1 < R2
R1 > R2
R1 ≥ R2
23318.A particle is performing a U.C.M. Which is the wrong statement regarding its motion?
The velocity vector is tangential to the circle
The acceleration vector is tangential to the circle
The acceleration vector is directed towards the centre of the circle
The velocity and acceleration vectors are perpendicular to each other
23319.A particle is performing U.C.M. along a circular path of radius r, with a uniform speed v. Its tangential and radial acceleration are
zero and infinite
$\dfrac{v^2}{r}$ and zero
zero and $\dfrac{v^2}{r}$
rω2 and infinite
23320.A particle moving in a circle of radius 25 cm at 2 revolutions per second. The acceleration of the particle is S.I. unit is
4$π$2
3$π$2
2$π$2
$π$2
23321.A particle of mass m is moving in a horizontal circle of radius R with uniform speed v. When it moves from one point to a diametrically opposite point its
kinetic energy changes by Mv2/4
momentum does not change
momentum changes by 2 Mv2
kinetic energy changes by Mv2
23322.A particle rests on the top of a hemisphere of radius R. The smallest horizontal velocity that must be imparted to the particle if it is to leave the hemisphere without sliding down is
$\sqrt{gR}$
$\sqrt{2gR}$
$\sqrt{3gR}$
$\sqrt{5gR}$
23323.A simple pendulum of mass m and length l stands in equilibrium in vertical position. The maximum horizontal velocity that should be given to the bob at the bottom so that it completes on revolution is
$\sqrt{lg}$
$\sqrt{2lg}$
$\sqrt{3lg}$
$\sqrt{5lg}$
23324.A particle revolves round a circular path. The acceleration of the particle is
along the circumference of the circle
along the tangent
along the radius
zero
23325.A satellite has mass m speed v and radius r, the force acting on it is:
zero
mrv2
$\dfrac{mv}{r}$
$\dfrac{mv^2}{r}$
23326.A car of mass 1000 kg moves on a circular road with a speed of 20 m/s. Its direction changes by 90° after traveling 628 m on the road. The centripetal force acting on the car is
500 N
1000 N
1500 N
2000 N
23327.A motor cyclist moving with a velocity of 75 km/hr on a flat road takes a turn on the road at a point where the radius of curvature of the road is 20 m. If the g is 10 m/s2 the maximum angle of banking with vertical for no skidding is
tan–1 (6)
tan–1 (2)
tan–1 (12)
tan–1 (4)
23328.A simple pendulum of effective length ‘l’ is kept in equilibrium in vertical position. What horizontal velocity should be given to its bob, so that it just completes a vertical circular motion?
$\sqrt{5gl}$
$\sqrt{3gl}$
$\sqrt{gl}$
$\sqrt{7gl}$
23329.A small body attached at the end of an inextensible string completes a vertical circle, then its
angular velocity remains constant
angular momentum remains constant
total mechanical energy remains constant
linear momentum remains constant
Explanation:
23330.A small body is to be moved inside a vertical circular tube of radius l. What minimum velocity should be imparted to it, as its lowest point so that it can just complete the vertical circle?
$\sqrt{5gl}$
$\sqrt{gl}$
$\sqrt{3gl}$
$\sqrt{4gl}$
23331.A stone attached to a rope of length l = 80 cm is rotated with a speed of 240 r.p.m. At the moment when the velocity is directed vertically upwards, the rope breaks. To what height does the stone rise further?
1.2 m
41.2 m
20.6 m
24.9 m
23332.A stone is tied to one end of a string. Holding the other end, the string is whirled in a horizontal plane with progressively increasing speed. It breaks at some speed because
gravitational forces of the earth is greater than the tension in string.
the required centripetal force is greater than the tension sustained by the string.
the required centripetal force is less than the tension in the string.
the centripetal force is greater than the weight of the stone.
23333.The K.E. (K) of a particle moving along a circle of radius r depends upon the distance covered (s) as K = as2. The centripetal force acting on the particle is given by
2as
2as2
$\dfrac{2as^2}{r}$
$\dfrac{2ar}{s^2}$
23334.A particle moves in a circular path of radius r, in half of its period. Its displacement and distance covered are,
2r, 2$π$r
r$\sqrt{2}$, $π$r
2r, $π$r
r, $π$r
23335.A stone of mass 250 gram, attached at the end of a string of length 1.25 m is whirled in a horizontal circle at a speed of 5 m/s. What is the tension in the string?
2.5 N
5 N
6 N
8 N
23336.A motor cyclist loops a vertical circular loop of diameter 18 m, without dropping down, even at the highest point of the loop. What should be his minimum speed at the lowest point of the loop?
10 m/s
16 m/s
21 m/s
30 m/s