Q.1.
railway tracks are banked on curves so that
-
29%
a)no frictional force may be produced between the track and wheels
-
57%
b) the train may not fall down inward
-
14%
c)necessary centripetal force may be obtained from the horizontal component of normal reaction due to the track
-
0%
d)none of the above
Q.2.
A motor cyclist rides on cylindrical wall of velodrome ( hollow metal cylinder kept with the axis vertical) of radius r rotating about its axis at the rate f rev/sec. the least coefficient of friction necessary so that he does not step down is
-
20%
a) g / (4π2f2r)
-
40%
b) (4π2f2r) / r
-
20%
c)(4π2f2) / gr
-
20%
d)gr/(4π2r2)
Explanation
Q.3.
If a particle of mass 'm' is moving in a horizontal circle of radius 'r' with a centripetal force ( -1/r2) the total energy is [ JIPMER 1998]
-
40%
a)-1/2r
-
60%
b) -1/r
-
0%
c)-2/r
-
0%
d)-4/r
Q.4.
A particle of mass m is executing uniform circular motion on a path of radius r. If p is the magnitude of its linear momentum, the radial force acting on the particle is : [ MPPMT 1994]
-
0%
a) pmr
-
40%
b) rm/p
-
20%
c) mp2 /r
-
40%
d) p2 / rm
Q.5.
A body of mass m hangs at one end of string of length l, the other end of which is fixed. It is given a horizontal velocity so that the string would just become slack, when it makes an angle of 60° with the upward drawn vertical. The tension in the string at this position is [ ISM Dhanbad 1994]
-
20%
a) 4.5 mg
-
20%
b) mg
-
20%
c)3m
-
40%
d)√3 mg
Explanation
Q.6.
A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a is varying with time t, a=k2rt2 where k is a constant. The power delivered to the particle by the forces acting on it is [ IIT 1994]
-
20%
a) 2πmk2r2t
-
20%
b) mk2r2t
-
60%
c)(mk4r2t5) / 3
-
0%
d)zero
Q.7.
The tension in the string revolving in a vertical circle with a mass m at the end which is .. [ EAMCET 1995]
-
0%
a) mv2 / r
-
60%
b) (mv2 / r) - mg
-
40%
c)(mv2 / r) + mg
-
0%
d)mg
Q.8.
A pendulum is suspended from the ceiling of a car rotating in ac circular path with an acceleration of 0.49m/sThe angle which the string makes with the vertical is
-
17%
a) tan-1 ( 1/√3)
-
33%
b) tan-1√3
-
33%
c) tan-1 0.05
-
17%
d) tan-1 0.005
Explanation
Q.9.
The string of pendulum of length l is displaced through 90° from the vertical and released. then the minimum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is [ MP 1986]
-
20%
a)mg
-
40%
b) 3mg
-
20%
c)5mg
-
20%
d)6mg
Explanation
Q.10.
A stone of mass 1kg tied to a light inextensible string of length L=(10/3) m is whirling in a circular path of radius L in a vertical plane If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be 10 m/s2 the speed of the stone at the highest point of the circle is [ CPMT 1998]
-
0%
a) 20 m/s
-
60%
b) 10√3 m/s
-
20%
c)5√2 m/s
-
20%
d)10 m/s
Explanation
Q.11.
A heavy small sized sphere is suspended by a string of length l. the sphere rotates uniformly in horizontal circle with the string making angle θ with the vertical. Then the time period of conical pendulum is
-
0%
a)
-
60%
b)
-
20%
c)
-
20%
d)
Explanation
Q.12.
A piece of stone is projected at angle θ with velocity u. If it executes nearly a circular motion at its maximum point for short time, the radius of the circle will be [CPMT]
-
0%
a) u2 / g
-
75%
b) (u2cos2θ) / g
-
0%
c) (u2sin2θ) / g
-
25%
d) (u2cos2θ) / 2g
Q.13.
A block of mass M is tied to one end of mass less rope. The other end of the rope is in the hands of a man of mass 2M as shown in figure. The block and man are resting on a rough wedge of mass M as shown in figure. The whole system is resting on smooth horizontal surface. The man pulls the rope. Pulley is mass less and frictionless. What is the displacement of the wedge when the block meets the pulley ( man does not leave his position during the pull)
-
25%
a)0.5 m
-
25%
b) 1 m
-
25%
c)zero
-
25%
d)23 m
Explanation
Q.14.
Two meteorites in free space are 8 m apart. Their masses are 7kg and 9kg. Then their centre of mass which lies on the line joining the centre of two bodies is
-
0%
a) At 4 meters from each meteorites
-
50%
b) At 3.5 meter from meteorites with a mass of 9kg
-
25%
c)At 3.5 meter from the meteorites with mass 7 kg
-
25%
d)At 8 meters from one end and 16 meter from the other end
Q.15.
Two point masses m1 and m2 ( m >m2) attract each other with force which is inversely proportional to the square of the distance between them. The particles which are initially at rest, when released have centre of mass of the system moves
-
0%
a)moves towards m1
-
25%
b) moves towards m2
-
50%
c)move at right angles to the line joining m1 and m2
-
25%
d)does not move at all
Q.16.
A heavy ball is thrown on rough horizontal surface in such a way that its slides with a speed Vo initially without rolling. It will roll without sliding when its speed falls to
-
0%
a) (2/7)Vo
-
0%
b) (3/7)Vo
-
50%
c) (5/7)Vo
-
50%
d) (7/5)Vo
Explanation
Q.17.
The centre of mass of a systems of two particles is
-
0%
a)on the line joining them and midway between them
-
50%
b) on the line joining them at a point whose distance from each particle is proportional to the square of the mass of that particle.
-
25%
c)on the line joining them at a point whose distance from each particle inversely proportional to the mass of that particle.
-
25%
d)On the line joining them at a point whose distance from each particle is proportional to the mass of that particle.
Q.18.
A solid sphere is rotating about a diameter due to increase in room temperature, its volume increases by 0.5%, If no external torque acts. The angular speed of the sphere will.
-
0%
a)increase by nearly 1/3 %
-
50%
b)decrease by nearly 1/3 %
-
50%
c)increase by nearly (1/2 %
-
0%
d)decrease nearly by (1/2) %
Q.19.
A circular disc of radius R is free to oscillate about an axis passing through a point on its rim and perpendicular to its plane. The disc is turned through an angle of 60? and released. Its angularvelocity when it reaches the equilibrium position will be__
-
25%
a)
-
75%
b)
-
0%
c)
-
0%
d)
Explanation
Q.20.
The moment of inertia of a hollow sphere of mass M and inner and outer radii R and 2R about the axis passing through its centre and perpendicular to its plane is
-
0%
a)
-
25%
b)
-
25%
c)
-
50%
d)
Explanation
Q.21.
Two strings of length l = 0.5 m each are connected to a block of a mass m = 2 kg at one end and their ends are attached to the point A and B, 0.5 m apart on a vertical pole which rotates with a constant angular velocity ω = 7 rad/sec. Find ratio T1 / T2 . Tension in the upper sting is (T1) and tension in lower string is (T2) [ use g = 9.8 m/s2]
-
0%
a) 1
-
25%
b) 3
-
50%
c) 9
-
25%
d) 6
Explanation
Q.22.
From a uniform circular disc of radius R, a circular disc of radius R/6 and having centre at a distance +R/2 from the centre of the disc is removed. Determine the centre of mass of remaining
-
25%
a) -R/70
-
75%
b) +R/70
-
0%
c) -R/7
-
0%
d) +R/7
Explanation
Q.23.
A wheel is rotating at 900 rpm about its axis. When power is cut off it comes to rest in 1 minute, the angular retardation in rad / sec is ___
-
80%
a) π/2
-
0%
b) π/4
-
0%
c) π/6
-
20%
d) π/ 8
Q.24.
A thin uniform rod AB of mass M and length L is hinged at one end A to the horizontal floor. Initially it stands vertically and becomes horizontal. It is allowed to fall freely on the floor in the vertical plane. The angular velocity of the rod when its end B strikes the floor is ____
-
25%
a) √(g/l)
-
0%
b) √(2g/l)
-
50%
c) √(3g/l)
-
25%
d) 2√(g/l)
Explanation
Q.25.
A circular plate of uniform thickness has a diameter of 56 cm. A circular portion of diameter42 cm. is removed from +ve x edge of the plate. Find the position of centre of mass of theremaining portion with respect to centre of mass of whole plate.
-
25%
a)- 7 cm
-
25%
b)+ 9 cm
-
25%
c)- 9 cm
-
25%
d)+ 7 cm
Explanation
Q.26.
A particle performing uniform circular motion has angular momentum L., its angular frequency is doubled and its K.E. halved, then the new angular momentum is
-
0%
a) L/2
-
50%
b)L/4
-
50%
c)2L
-
0%
d)4L
Q.27.
A solid sphere is rotating about a diameter at an angular velocity ω. if it cools so that its radius reduces to 1/n of its original value. Its angular velocity becomes_____
-
25%
a) ω/n
-
25%
b) ω/n2
-
25%
c)nω
-
25%
d)n2ω
Q.28.
Two blocks of masses 10 kg an 4 kg are connected by a spring of negligible mass and placedon a frictionless horizontal surface. An impulse gives velocity of 14 m/s to the heavier block inthe direction of the lighter block. The velocity of the centre of mass is
-
50%
a) 30 m/s
-
0%
b) 20 m/s
-
25%
c) 10 m/s
-
25%
d) 5 m/s
Explanation
Q.29.
A circular disc of mass m and radius r is rolling on a smooth horizontal surface with a constant speed v. Its kinetic energy is _____
-
0%
a)(1/4) mv2
-
25%
b) (1/2) mv2
-
75%
c)(3/4) mv2
-
0%
d) mv2
Q.30.
A body of mass m is tied to one end of spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is one centimeter. If the angularvelocity is doubted, the elongation in the spring is 5 cm. The original length of spring is...
-
0%
a)16 cm
-
50%
b)15 cm
-
50%
c)14 cm
-
0%
d)13 cm