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May 2022

Home2022MayPage 36

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 (164)

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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Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry’s standard dummy...

At what distance from the centre of the earth, the value of acceleration due to gravity g will be half that on the surface (R = radius of earth)

(a)  2 R                                      (b)  R (c)   1.414 R                              (d)  0.414 R Answer:  d (6)

5. Nylon is not a

a. Condensation polymer b. Polyamide c. Copolymer d. Homopolymer Ans. d (7)

4. Polyethylene is

a. Random copolymer b. Homopolymer c. Alternate copolymer d. Crosslinked copolymer Ans. b (14)

3. Which of the following is an example of condensation polymer

a. Nylon b. Bakelite c. Urea-formaldehyde resin d. all of these Ans. d (18)

2. A thermoplastic among the following is

a. Bakelite b. Polystyrene c. Terylene d. Urea-formaldehyde resin e. Nylon Ans. b (12)

1. Correct statement for thermoplastic polymer is

a. It does not become soft on heating under pressure b. it can not be remoulded c. it is either...

The acceleration due to gravity near the surface of a planet of radius R and density d is proportional to

(a)    d/R2                                 (b)  dR2...

What will be the acceleration due to gravity at height h if h >> R. Where R is radius of earth and g is acceleration due to gravity on the surface of earth

(a)   g/(1 + h/R  )2                     (b)  g ( 1 – 2h/R...

Weight of a body is maximum at

(a)  Moon                                  (b)  Poles of earth (c)   Equator of earth               (d)  Centre of earth Answer: b (6)

A man can jump to a height of 1.5 m on a planet A. What is the height he may be able to jump on another planet whose density and radius are, respectively, one-quarter and one-third that of planet A

(a)  1.5 m                                  (b)  15 m (c)   18 m                                   (d)  28 m Answer: c (5)

A thin wire of length L and uniform linear mass density ρ  is bent into a circular loop with centre at O as shown.  The moment of inertia of the loop about the axis XX’  is    

  (a)      ρL3/8π2 (b)    ρL3/16π2 (c)     5ρL3/16π2 (d)     3ρL3/8π2 Ans. d (10)

63. Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1 : 3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratio

(a)  1 : 3 (b)  3 : 1 (c)   1 : 9 (d)  9 : 1 Ans. b (56)

The angular speed of earth, so that the object on equator may appear weightless (g = 10 m/s2 , is , radius of earth 6400 km)

(a)     1.25×10-3 rad/sec          (b)  1.56 ×10-3 rad/sec (c) 1.25×10-1 rad/sec            (d) ...

68. A thin wire of length l and mass M is bent in the form of a semi-circle. What is its moment of inertia about an axis passing through the ends of the wire

(a)         ML2/2 (b)         ML2/π2 (c)         2ML2/ π2 (d)       2ML2/2π2 Ans. d (5)

Assume that the acceleration due to gravity on the surface of the moon is 0.2 times the acceleration due to gravity on the surface of the earth. If  Re is the maximum range of a projectile on the earth’s surface, what is the maximum range on the surface of the moon for the same velocity of projection

(a)   0.2 Re                               (b) 2...

If the mass of earth is 80 times of that of a planet and diameter is double that of planet and ‘g’ on earth is 9.8 m/s2 , then the value of ‘g’ on that planet is

(a)    4.9 m/s2                    (b)  0.98 m/s2 (c)   0.49  m/s2   ...

R and r are the radii of the earth and moon respectively. pe  and  pm are the densities of earth and moon respectively. The ratio of the accelerations due to gravity on the surfaces of earth and moon is

(a)      R/r  pe/ pm                 (b)  r/R  pe/ pm (c)      r/R  pe/ pm ...

66. Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of

(a)    0.4 m  from mass of 0.3 kg (b)   0.98 from mass of 0.3 kg (c)   0.70 m  from...

65. If solid sphere and solid cylinder of same radius and density rotate about their own axis, the moment of inertia will be greater for (L = R)

(a)  Solid sphere (b)  Solid cylinder (c)   Both (d)  Equal both Ans. a (50)

Assuming earth to be a sphere of a uniform density, what is the value of gravitational acceleration in a mine 100 km below the earth’s surface (Given R = 6400 km)

(a)      9.66 m/s2                      (b)  7.64 m/s2 (c)   5.06m/s2...

The angular velocity of the earth with which it has to rotate so that acceleration due to gravity on 60o latitude becomes zero is (Radius of earth = 6400 km. At the poles g=10 ms-2)

(a)  2.5 × 10-3 rad /s               (b)  5.0 × 10-1 rad /s (c)  10  ×...

62. One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

(a)    1/2 MR2 (b)    1/4 MR2 (c)  1/8 MR2 (d) √2 MR2 Ans. a (8)

61. From a uniform wire, two circular loops are made (i) P of radius r and (ii) Q of radius nr. If the moment of inertia of Q about an axis passing through its centre and perpendicular to its plane is 8 times that of P about a similar axis, the value of n is (diameter of the wire is very much smaller than r or nr)

(a)  8 (b)  6 (c)  4 (d)  2 Ans. d (9)

An object weights 72 N on earth. Its weight at a height of R/2 from earth is

(a)  32 N                                   (b)  56 N (c)    72 N                   ...

The height of the point vertically above the earth’s surface, at which acceleration due to gravity becomes 1% of its value at the surface is (Radius of the earth = R)

(a)  8 R                                      (b)  9 R (c)   10 R                                    (d)  20 R Answer: b (9)

If the Earth losses its gravity, then for a body

(a)  Weight becomes zero, but not the mass (b)  Mass becomes zero, but not the weight (c)   Both mass and...

At what height from the ground will the value of ‘g’ be the same as that in 10 km deep mine below the surface of earth

(a)  20 km                                 (b)  10 km (c)   15 km                                 (d)  5 km Answer: a (10)

Acceleration due to gravity is ‘g’ on the surface of the earth. The value of acceleration due to gravity at a height of 32 km above earth’s surface is (Radius of the earth = 6400 km)

(a)  0.9 g                                   (b)  0.99 g (c)   0.8 g                                   (d)  1.01 g Answer: b (18)

What should be the velocity of earth due to rotation about its own axis so that the weight at equator become 3/5 of initial value. Radius of earth on equator is 6400 km

(a)    7.4 × 10-4 rad /sec                    (b)  6.7 × 10-4...

Mass of moon is   7.34 ×1022  kg. If the acceleration due to gravity on the moon is  1.4 m/s2 , the radius of the moon is (G = 6.667×10-11 Nm2 /kg2)

(a)    0.56 × 104                 (b) 1.87  × 106 (c)    1.92 × 106...

If mass of a body is M on the earth surface, then the mass of the same body on the moon surface is

(a)      M/6                                 (b)  Zero (c)  ...

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