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Gravitation Physics - Gravitation

Uttarakhand Board (UBSE) - STD 11 Science - Physics (Uttarakhand - English Medium). 509 questions in this chapter.

Question types

Gravitation question types

509 questions across 6 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

509
Questions
6
Question groups
5
Question types
Sample Questions

Gravitation questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
The kinetic energy of the satellite in a circular orbit with speed vis given as:
  • A
    $\text{KE}=\frac{-\text{GmM}_\text{e}}{2(\text{R}_\text{e}+\text{h})}$
  • B
    $\text{KE}=\frac{\text{GmM}_\text{e}}{(\text{R}_\text{e}+\text{h})}$
  • ✓
    $\text{KE}=\frac{\text{GmM}_\text{e}}{2(\text{R}_\text{e}+\text{h})}$
  • D
    $\text{KE}=-\frac12\text{mv}^2$

Answer: C.

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Q 2M.C.Q (1 Marks)1 Mark
A particle of mass $m$ is at the surface of the earth of radius $R.$ It is lifted to a heighth abov the surface of the earth. The gain in gravitational potential energy of the particle is:
  • A
    $\frac{\text{mgh}}{\big(1-\frac{\text{h}}{\text{R}}\big)}$
  • B
    $\frac{\text{mgh}}{\big(1+\frac{\text{h}}{\text{R}}\big)}$
  • C
    $\frac{\text{mghR}}{(\text{R}+\text{h})}$
  • ✓
    $\text{Both (b) and (c)}$

Answer: D.

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Q 3M.C.Q (1 Marks)1 Mark
As observed from earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from earth, this would.
  • A
    Be similarly true.
  • B
    Not be true because the force between earth and mercury is not inverse square law.
  • ✓
    Not be true because the major gravitational force on mercury is due to sun.
  • D
    Not be true because mercury is influenced by forces other than gravitational forces.

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark
If the gravitation force on body 1 due to 2 is given by $F_2$ and on body 2 due to 1 is given as $F_1$, then
  • A
    $F_{12}=F_{21}$
  • ✓
    $F_{12}=-F_{21}$
  • C
    $\text{F}_{12}=\frac{\text{F}_{21}}{4}$
  • D
    None of the above.

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark
A point mass $m$ is placed outside a hollow spherical shell of mass $M$ and uniform density at a distanced from centre of the big sphere.Gravitational force on point mass mat $P$ is:
  • ✓
    $\frac{\text{GmM}}{\text{d}^2}$
  • B
    Zero.
  • C
    $\frac{2\text{GmM}}{\text{d}^2}$
  • D
    Data insufficient.

Answer: A.

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Q 61 Marks Question1 Mark
Choose the correct alternative: The formula $-\text{G Mm}\Big(\frac{1}{\text{r}_2}-\frac{1}{\text{r}_1}\Big)$ is more/ less accurate than the formula mg(${\text{r}_2}$ - ${\text{r}_1}$) for the difference of potential energy between two points ${\text{r}_2}$ and ${\text{r}_1}$ distance away from the centre of the earth.
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Q 71 Marks Question1 Mark
A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (a) linear speed, (b) angular speed, (c) angular momentum, (d) kinetic energy, (e) potential energy, (f) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.
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Q 101 Marks Question1 Mark
Choose the correct alternative: Acceleration due to gravity increases/ decreases with increasing depth (assume the earth to be a sphere of uniform density).
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Q 112 Marks Questions2 Marks
Choose the correct alternative: If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic/ potential energy.
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Q 122 Marks Questions2 Marks
Answer the following: An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?
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Q 132 Marks Questions2 Marks
Answer the following: You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
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Q 142 Marks Questions2 Marks
Answer the following: If you compare the gravitational force on the earth due to the sun to that due to the moon, you would find that the Sun’s pull is greater than the moon’s pull. (you can check this yourself using the data available in the succeeding exercises). However, the tidal effect of the moon’s pull is greater than the tidal effect of sun. Why?
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Q 163 Marks Question3 Marks
Two stars each of one solar mass ($= 2 \times 10^{30}kg$) are approaching each other for a head on collision. When they are a distance $10^9km$, their speeds are negligible. What is the speed with which they collide? The radius of each star is $10^4km.$ Assume the stars to remain undistorted until they collide. (Use the known value of G).
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Q 173 Marks Question3 Marks
As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly $36,000km$ from the surface of the earth. What is the potential due to earth’s gravity at the site of this satellite? (Take the potential energy at infinity to be zero). Mass of the earth = $6.0 \times 10^{24}kg$, radius = $6400km$.
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Q 183 Marks Question3 Marks
Two heavy spheres each of mass $100kg$ and radius $0.10m$ are placed $1.0m$ apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centres of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?
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Q 203 Marks Question3 Marks
A rocket is fired from the earth towards the sun. At what distance from the earth's centre is the gravitational force on the rocket zero? Mass of the sun $=2 \times 10^{30} \mathrm{~kg}$, mass of the earth $=6 \times 10^{24} \mathrm{~kg}$. Neglect the effect of other planets etc. (orbital radius $=1.5 \times 10^{11} \mathrm{~m}$ ).
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Q 225 Marks Questions5 Marks
Does the escape speed of a body from the earth depend on (a) the mass of the body, (b) the location from where it is projected, (c) the direction of projection, (d) the height of the location from where the body is launched?
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Q 235 Marks Questions5 Marks
Which of the following symptoms is likely to afflict an astronaut in space (a) swollen feet, (b) swollen face, (c) headache, (d) orientational problem.
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Q 245 Marks Questions5 Marks
A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence? Mass of the satellite $=200 \mathrm{~kg}$; mass of the earth $=6.0 \times$ $10^{24} \mathrm{~kg}$; radius of the earth $=6.4 \times 10^6 \mathrm{~m} ; \mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \mathrm{~m}^2 \mathrm{~kg}^{-2}$.
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Q 255 Marks Questions5 Marks
Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?
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Q 26Case study (4 Marks)4 Marks
Read the passage given below and answer the following questions from 1 to 5. Cavendish’s Experiment The figure shows the schematic drawing of Cavendish’s experiment to determine the value of the gravitational constant. The bar AB has two small lead spheres attached at its ends. The bar is suspended from a rigid support by a fine wire. Two large lead spheres are brought close to the small ones but on opposite sides as shown. The value of G from this experiment came to be $6.67\times10^{-11}\frac{\text{N-m}^2}{\text{Kg}^2}$
  1. The big spheres attract the nearby small ones by a force which is:
  1. equal and opposite
  2. equal but in same direction
  3. unequal and opposite
  4. None of the above
  1. The net force on the bar is:
  1. non-zero
  2. zero
  3. Data insufficient
  4. None of these
  1. The net torque on the bar is:
  1. zero
  2. non-zero
  3. F times the length of the bar, where F is the force of attraction between a big sphere and its neighbouring
  4. Both (b) and (c)
  1. The torque produces twist in the suspended wire. The twisting stops when:
  1. restoring torque of the wire equals the gravitational torque
  2. restoring torque of the wire exceeds the gravitational torque
  3. the gravitational torque exceeds the restoring torque of the wire
  4. None of the above
  1. After Cavendish’s experiment, there have been given suggestions that the value of the gravitational constant G becomes smaller when considered over very large time period (in billions of years) in the future. If that happens, for our earth:
  1. nothing will change
  2. we will become hotter after billions of years
  3. we will be going around but not strictly in closed orbits
  4. None of the above
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Q 27Case study (4 Marks)4 Marks
Read the passage given below and answer the following questions from 1 to 5. LAW OF ORBIT: The orbit of every planet is an ellipse around the sun with sun at one of the two foci of ellipse.
LAW OF AREAS: The line that joins a planet to the sun sweeps out equal areas in equal intervals of time. Area covered by the planet while revolving around the sun will be equal in equal intervals of time. This means the rate of change of area with time is constant. LAW OF PERIOD: According to this law the square of time period of a planet is directly proportional to the cube of the semi-major axis of its orbit. Suppose earth is revolving around the sun then the square of the time period (time taken to complete one revolution around sun) is directly proportional to the cube of the semi major axis. It is known as Law of Periods as it is dependent on the time period of planets. Answer the following.
  1. Keplers second law is knows as:
  1. Law of period
  2. Law of area
  3. Law of gravity
  4. None of these
  1. Keplers third law is knows as:
  1. Law of period
  2. Law of area
  3. Law of gravity
  4. None of these
  1. The velocity of a planet is constant throughout its elliptical trajectory in an orbit.
  1. True
  2. False
  3. None of these
  1. State Kepler’s second law of planetary motion.
  1. Two objects of masses $5kg$ and $10 kg$ separated by distance 10m. What is gravitational force between them?
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Q 28Case study (4 Marks)4 Marks
Read the passage given below and answer the following questions from 1 to 5. Acceleration due to gravity The acceleration for any object moving under the sole influence of gravity is known as acceleration due to gravity. So, for an object of mass m, the acceleration experienced by it is usually denoted by the symbol g which is related to F by Newton’s second law by relation F = mg Thus, $\text{g}=\frac{\text{F}}{\text{m}}=\frac{{\text{Gm}_\text{e}}}{\text{R}^2_\text{e}}$ Acceleration g is readily measurable as Re is a known quantity. The measurement ofG by Cavendish’s experiment (or otherwise), combined with knowledge of g and Re enables one to estimate $M_e$ from the above equation. This is the reason why there is a popular statement regarding Cavendish “Cavendish weighed the earth”. The value of g decrease as we go upwards from the earth’s surface or downwards, but it is maximum at its surface.
  1. If g is the acceleration due to gravity at the surface of the earth, the force acting on the particle of mass m placed at the surface is:
  1. mg
  2. $\frac{\text{GmM}\theta}{\text{R}^2_\text{e}}$
  3. Data insufficient
  4. Both (a) and (b)
  1. The weight of a body at the centre of earth is:
  1. same as on the surface of earth
  2. same as on the poles
  3. same as on the equator
  4. None of the above
  1. If the mass of the sun is ten times smaller and gravitational constant G is ten times larger in magnitude, then for earth:
  1. walking on ground would become more easy
  2. acceleration due to gravity on the earth will not change
  3. raindrops will fall much slower
  4. airplanes will have to travel much faster
  1. Suppose, the acceleration due to gravity at the earth’s surface is $10 ms^{-2}$ and at the surface of mars, it is $4.0 ms ^{-2}$ 60kg passenger goes from the earth to the mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which curve best represents the weight (net gravitational force) of the passenger as a function of time?
  1. A
  2. B
  3. C
  4. D
  1. If the mass of the earth is doubled and its radius halved, then new acceleration due to the gravity $\acute{\text{g}}$ is:
  1. $\acute{\text{g}}=4\text{g}$
  2. $\acute{\text{g}}=8\text{g}$
  3. $​​\acute{g}=\text{g}$
  4. $\acute{\text{g}}=16\text{g}$
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Q 29Case study (4 Marks)4 Marks
Read the passage given below and answer the following questions from 1 to 5. We know that the earth attracts every object with a certain force and this force depends on the mass (m) of the object and the acceleration due to the gravity (g). The weight of an object is the force with which it is attracted towards the earth. Mathematically Where, W = weight of object m = mass of object g = acceleration due to the gravitational force As the weight of an object is the force with which it is attracted towards the earth, the SI unit of weight is the same as that of force, that is, Newton (N). The weight is a force acting vertically downwards; it has both magnitude and direction. We have learnt that the value of g is constant at a given place. Therefore at a given place, the weight of an object is directly proportional to the mass, say m, of the object, that is, W α m. It is due to this reason that at a given place, we can use the weight of an object as a measure of its mass. Answer the following questions.
  1. Dimensions of acceleration due to the gravity (g) is:
  1. $[ML^1 T^{-2}]$
  2. $[ML^{-1} T^{-2}]$
  3. $[ML^1 T^{-3}]$
  4. None of these
  1. SI unit of weight is same as:
  1. Force
  2. Mass
  3. Acceleration due to gravity
  4. None of these
  1. Which of the following has same unit?
  1. Mass and weight
  2. Weight and force
  3. Pressure and stress
  4. Both b and c
  1. Whether weight is scalar quantity or vector quantity? Justify your answer.
  1. Differentiate between mass and weight.
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Q 30Case study (4 Marks)4 Marks
Read the passage given below and answer the following questions from 1 to 5. If a stone is thrown by hand, we see it falls back to the earth. Of course using machines we can shoot an object with much greater speeds and with greater and greater initial speed, the object scales higher and higher heights. A natural query that arises in our mind is the following: can we throw an object with such high initial speeds that it does not fall back to the earth ? Thus minimum speed required to throw object to infinity away from earth’s gravitational field is called escape velocity. $\text{V}_{\text{e}}=\sqrt{(2\text{gr})}$ Where g is acceleration due to gravity and r is radius of earth and after solving ve $11.2$ km/s. This is called the escape speed, sometimes loosely called the escape velocity. This applies equally well to an object thrown from the surface of the moon with g replaced by the acceleration due to Moon’s gravity on its surface and r replaced by the radius of the moon. Both are smaller than their values on earth and the escape speed for the moon turns out to be $2.3$ km/s, about five times smaller. This is the reason that moon has no atmosphere. Gas molecules if formed on the surface of the moon having velocities larger than this will escape the gravitational pull of the moon. Earth satellites are objects which revolve around the earth. Their motion is very similar to the motion of planets around the Sun and hence Kepler’s laws of planetary motion are equally applicable to them. In particular, their orbits around the earth are circular or elliptic. Moon is the only natural satellite of the earth with a near circular orbit with a time period of approximately $27.3$ days which is also roughly equal to the rotational period of the moon about its own axis.
  1. Time period of moon is:
  1. 27.3 days
  2. 20 days
  3. 85 days
  4. None of these
  1. Escape velocity from earth is given by:
  1. 20 km/s
  2. 11.2 km/s
  3. 2 km/s
  4. None of these
  1. Define escape velocity. Give its formula.
  1. Why moon don’t Have any atmosphere?
  1. What is satellite? Which law governs them?
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