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May 19, 2022

Home2022May19Page 7

What should be the angular speed of earth, so that body lying on equator may appear weightlessness ( g = 10 m/s2, R=6400 km )

(a)      1/800  rad/s                               (b) ...

A person will get more quantity of matter in kg –wt. at

(a)      Poles                               (b)  At latitude of...

89. A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be

(a)    K2/R2 (b)    K2/K2+R2 (c)     R2/K2+R2 (d)     K2+R2/R2 Ans. b (9)

87. A stick of length l and mass M lies on a frictionless horizontal surface on which it is free to move in any way. A ball of mass m moving with speed v collides elastically with the stick as shown in the figure. If after the collision ball comes to rest, then what should be the mass of the ball

(a)  m=2M (b) m=M (c)  m=M/2 (d) m=m/4 Ans. d (13)

A cubical block of side α is moving with velocity v on a horizontal smooth plane as shown. It hits a ridge at point O. The angular speed of the block after it hits O is

  (a)   3v/4a (b)  3v/2a (c)  √3v/√2a (d)  Zero Ans. a (7)

84. A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω . Another disc of same dimension but of mass M/4 is placed gently on the first disc coaxially. The angular velocity of the system now is

(a)   2ω/5 (b) 2ω/√5 (c) 4ω/5 (d) 4ω/√5 Ans. c (18)

82. A uniform disc of mass M and radius R is rotating about a horizontal axis passing through its centre with angular velocity ω. A piece of mass m breaks from the disc and flies off vertically upwards. The angular speed of the disc will be

(a)    (M-2m)ω/(M-m) (b)    (M+2m)ω/(M+m) (c)    (M-2m)ω/(M+m) (d)   (M+2m)ω/(M-m) Ans. a (223)

91. The total kinetic energy of a body of mass 10 kg and radius 0.5 m moving with a velocity of 2 m/s without slipping is 32.8 joule. The radius of gyration of the body is

(a)           0.25 m (b)          0.2 m      (c)           0.5 m (d)          0.4 m Ans. d (43)

88. In a playground there is a merry-go-round of mass 120 kg and radius 4 m. The radius of gyration is 3m. A child of mass 30 kg runs at a speed of 5 m/sec tangent to the rim of the merry-go-round when it is at rest and then jumps on it. Neglect friction and find the angular velocity of the merry-go-round and child

(a)           0.2 rad/sec (b)          0.1 rad/sec (c)           0.4 rad/sec (d)          0.8 rad/sec Ans. c (95)

83. A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved

(a)  Centre of the circle (b)  On the circumference of the circle (c)   Inside the circle (d)  Outside the circle...

81. A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by 1%. Its angular speed

(a)   Will increase approximately by 1% (b)   Will decrease approximately by 1% (c)   Will decrease approximately by 0.67% (d)  Will...

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ω. Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity

(a)  ω(M-2m) /(M+2m) (b)  ωM/M+2m) (c)   ωM/M+m (d)  ω(M+2m)/M Ans. b (49)

78. An equilateral triangle ABC formed from a uniform wire has two small identical beads initially located at A. The triangle is set rotating about the vertical axis AO. Then the beads are released from rest simultaneously and allowed to slide down, one along AB and the other along AC as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down, are

      (a)  Angular velocity and total energy (kinetic and potential) (b)  Total angular momentum and total energy (c)  ...

77. A uniform heavy disc is rotating at constant angular velocity ω about a vertical axis through its centre and perpendicular to the plane of the disc. Let L be its angular momentum.  A lump of plasticine is dropped vertically on the disc and sticks to it.  Which will be constant

(a)    w (b)   w and L both (c)   L only (d)  Neither w nor L Ans. c (49)

76.

Two rigid bodies A and B rotate with rotational kinetic energies EA and EB respectively. The moments of inertia of...

75. A particle of mass m moves along line PC with velocity v as shown. What is the angular momentum of the particle about O

    (a)  mvL (b)  mvl (c)   mvr (d)  Zero Ans. b (6)

The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be

(a)    2R                                   ...

74. A disc is rotating with an angular speed of ω. If a child sits on it, which of the following is conserved

(a)  Kinetic energy (b)  Potential energy (c)   Linear momentum (d)  Angular momentum Ans. d (11)

73. The motion of planets in the solar system is an example of the conservation of

(a) Mass (b) Linear momentum (c)   Angular momentum (d)  Energy Ans. c (8)

If both the mass and the radius of the earth decrease by 1%, the value of the acceleration due to gravity will

(a)      Decrease by 1%                       (b)  Increase by 1% (c)   Increase by 2%                 (d)  Remain unchanged Answer:  b (9)

73. Weight of a body of mass m decreases by 1% when it is raised to height h above the earth’s surface. If the body is taken to a depth h in a mine, change in its weight is

(a)  2% decrease                    (b)  0.5% decrease (c)   1% increase                      (d)  0.5% increase Answer: b (9)

The depth at which the effective value of acceleration due to gravity is  g/4 is

(a)  R                                         (b)  3R/4 (c)      R/2                       ...

72. A thin rod of length L and mass M is bent at the middle point O at an angle of 60 degree as shown in figure. The moment of inertia of the rod about an axis passing through O and perpendicular to the plane of the rod will be

    (a)  ML2/6 (b) ML2/12 (c) ML2/24 (d) ML2/3 Ans. b (39)

71. The acceleration of a body due to the attraction of the earth (radius R) at a distance 2 R from the surface of the earth is (g = acceleration due to gravity at the surface of the earth)

(a)    g/9                                   ...

Acceleration due to gravity on moon is 1/6 of the acceleration due to gravity on earth.  If the ratio of densities of earth  ( pe ) and moon ( pm )  is ( pe/pm )  = 5/3  then radius of moon Rm in terms of Re will be

(a)      5/18 Re                            (b)  1/6...

71. The moment of inertia I of a solid sphere having fixed volume depends upon its volume V as

(a)    I ∝  V (b)    I ∝   V2/3 (c)    I ∝ V5/3 (d)    I ∝   V3/2 Ans....

70. Four solids are shown in cross section. The sections have equal heights and equal maximum widths. They have the same mass. The one which has the largest rotational inertia about a perpendicular through the centre of mass is

Ans. a (170)

A research satellite of mass 200 kg circles the earth in an orbit of average radius 3R/2 where R is the radius of the earth. Assuming the gravitational pull on a mass of 1 kg on the earth’s surface to be 10 N, the pull on the satellite will be

(a)  880 N                                 (b)  889 N (c)   890 N                                 (d)  892 N Answer: a (7)

If the value of ‘g’ acceleration due to gravity, at earth surface is 10 m/s2 , its value in  m/s2  at the centre of the earth, which is assumed to be a sphere of radius ‘R’ metre and uniform mass density is

(a)  5                                         (b)  10/R (c)   10/2R                                (d)  Zero Answer: d (16)

The acceleration due to gravity at pole and equator can be related as

(a)    gp < ge                           (b)  gp =...

If the density of the earth is doubled keeping its radius constant then acceleration due to gravity will be (g=9.8 m/s2 )

(a)   19.6 m/s2                         (b)  9.8 m/s2 (c)     ...

A body weight W newton at the surface of the earth. Its weight at a height equal to half the radius of the earth will be

(a)    W/2                                   (b) ...

The acceleration due to gravity is g at a point distant r from the centre of earth of radius R. If  r < R , then

(a)       g ∝ r                            (b) ...

If density of earth increased 4 times and its radius become half of what it is, our weight will

(a)  Be four times its present value (b)  Be doubled (c)   Remain same (d)  Be halved Answer:  b (5)
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