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2022

Home2022Page 78

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)  ...

If radius of the earth contracts 2% and its mass remains the same, then weight of the body at the earth surface

(a)      Will decrease                     (b)  Will increase (c)   Will remain the same      ...

If the radius of the earth shrinks by 1.5% (mass remaining same), then the value of acceleration due to gravity changes by

(a)      1%                                  (b)   ...

Where will it be profitable to purchase 1 kilogram sugar

(a)      At poles                          (b)  At equator (c)   At...

24. Assertion : A body subjected to three concurrent forces cannot be in equilibrium. Reason : If large number of concurrent forces acting on the same point, then the point will be in equilibrium, if sum of all the forces is equal to zero.

(a)       If both assertion and reason are true and the reason is the correct explanation of the assertion. (b)       If...

25. Assertion : Impulse and momentum have different dimensions. Reason : From Newton’s second law of motion, impulse is equal to change in momentum.

(a)       If both assertion and reason are true and the reason is the correct explanation of the assertion. (b)       If...

23. Assertion : A table cloth can be pulled from a table without dislodging the dishes. Reason : To every action there is an equal and opposite reaction.

(a)       If both assertion and reason are true and the reason is the correct explanation of the assertion. (b)       If...

22. Assertion : A reference frame attached to earth is an inertial frame of reference. Reason : The reference frame which has zero acceleration is called a non inertial frame of reference.

(a)       If both assertion and reason are true and the reason is the correct explanation of the assertion. (b)       If...

21. Assertion : Newton’s third law of motion is applicable only when bodies are in motion. Reason : Newton’s third law applies to all types of forces, e.g. gravitational, electric or magnetic forces etc.

(a)       If both assertion and reason are true and the reason is the correct explanation of the assertion. (b)       If...

Let g be the acceleration due to gravity at earth’s surface and K be the rotational kinetic energy of the earth. Suppose the earth’s radius decreases by 2% keeping all other quantities same, then

(a)      g decreases by 2% and K decreases by 4% (b)  g decreases by 4% and K increases by 2%...

Radius of earth is around 6000 km. The weight of body at height of 6000 km from earth surface becomes

(a)      Half                                  (b)   ...

A satellite revolves around the earth in an elliptical orbit. Its speed

(a)      Is the same at all points in the orbit (b)  Is greatest when it is closest to the earth...

Alginic acid is obtained from

(a)  Red algae                           (b)  Green algae (c)   Diatoms                             (d)  Brown algae Ans. d (11)

20. Assertion : Linear momentum of a body changes even when it is moving uniformly in a circle. Reason : In uniform circular motion velocity remain constant.

(a)       If both assertion and reason are true and the reason is the correct explanation of the assertion. (b)       If...

A small satellite is revolving near earth’s surface. Its orbital velocity will be nearly

(a)      8 km/sec                            (b)  11.2 km/sec (c)   4 km/sec                            (d)  6 km/sec Answer: a (12)

19. Assertion : The acceleration produced by a force in the motion of a body depends only upon its mass. Reason : Larger is the mass of the body, lesser will be the acceleration produced.

(a)       If both assertion and reason are true and the reason is the correct explanation of the assertion. (b)       If...

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